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REVIEW 4 major objections 4 minor 101 references

Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Applying the Kramers–Wannier duality operator to the 2D XY model's even-parity stripe states yields exact low-entanglement eigenstates — quantum many-body scars — in the dual $\mathbb{Z}_2$ lattice gauge theory.

desk verdict Sound exact construction of 2D XY scars and a duality transfer theorem; the abstract overreaches on the kagome/dice case. read the letter →

arxiv 2505.21921 v3 pith:I674IXJV submitted 2025-05-28 cond-mat.str-el cond-mat.stat-mechquant-ph

Yuan Miao , Linhao Li , Hosho Katsura , Masahito Yamazaki This is my paper
classification cond-mat.str-elcond-mat.stat-mechquant-ph
keywords quantummany-bodyscarslatticegaugetheoryKramers-WannierdualityXYmodelentanglemententropyprojectedentangled-pairoperatorergodicitybreakingstripeeigenstates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a two-dimensional $\mathbb{Z}_2$ lattice gauge theory hosts exact quantum many-body scars — special low-entanglement eigenstates sitting in the middle of the spectrum that violate the usual thermalization expectations. The route is a duality: the gauge model is the Kramers–Wannier dual of the spin-1/2 XY model, and the XY model itself carries a tower of exact eigenstates built from staggered superpositions of one magnon along straight 'stripes,' where hopping terms cancel pairwise. Applying the duality operator to the even-parity stripe states gives exact eigenstates of the gauge theory with the same energies, because the operator intertwines the two Hamiltonians ($D H_{XY} = H_{\rm dual} D$). The paper's further claim is that the duality preserves low entanglement, so the dual states are scars of the gauge model, not merely exact eigenstates. If correct, this supplies scarce higher-dimensional gauge-theory examples of scar physics and suggests a general recipe: gauging a symmetry can carry scars from one model to a dual one.

What carries the argument

Two objects carry the argument. First, the stripe states: staggered superpositions of a single magnon along a straight row of sites, $Q^{\pm}_S |\Downarrow\rangle$ with signs alternating across the bipartite lattice; their defining property is the cancelation mechanism by which the XY exchange term's two hopping paths around each square cancel, so $H_{XY}$ annihilates them, and only straight, mutually nonadjacent stripes are allowed. Second, the duality operator $D$: a generalized Kramers–Wannier map (dual spins live on edges of the dual lattice) realized as a projected entangled-pair operator (PEPO) with isometries, satisfying the intertwining relations $D H_{XY} = H_{\rm dual} D$ and $D H_Z = H D$, the projector identity $D^{\dagger}D = I + \prod \sigma^z$, and $D$ annihilating odd-parity states. The scar transfer then follows from the isomorphism $D$ induces between the even $\mathbb{Z}_2$-parity sector of the XY model and the even 1-form-symmetry sector of the gauge theory; the area-law claim for the dual states rests on the assertion, in Sec. 3.2, that the PEPO is a low-depth tensor network operator that preserves area-law entanglement scaling.

What would settle it

A concrete check would be to compute the von Neumann entanglement entropy of the dual state $D|\{S_1,\dots,S_n\}\rangle$ for a half-system bipartition on the torus (or via tensor-network contraction of the PEPO on increasingly large lattices) and compare its growth with subsystem size. If the entropy scales with the volume of the subsystem rather than its boundary, the paper's identification of these states as quantum many-body scars of the $\mathbb{Z}_2$ gauge model fails, even though Eq. (3.5) would still guarantee they are exact eigenstates.

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Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that the exact quantum many-body scars of the two-dimensional spin-1/2 XY model survive the generalized Kramers–Wannier duality and become exact quantum many-body scars of the dual $\mathbb{Z}_2$ lattice gauge model. In the XY model, the states $|\{S_1,\dots,S_n\}\rangle_{\pm}$, superpositions of $n$ up-spins placed on nonadjacent straight stripes with staggered signs, are exact eigenstates because every hopping contribution that moves a magnon is cancelled by an opposite-sign contribution from the neighbouring site; they form a tower of states with energies $(2n-N)h$ relative to the all-down vacuum and with entanglement entropy computable stripe by stripe. Gauging the $\mathbb{Z}_2$ 0-form symmetry produces the dual gauge theory, and the duality operator $D$ obeys $D H_{XY} = H_{\rm dual} D$ together with the projection identity $D^{\dagger}D = I + \prod \sigma^z$, making the even-parity subsector of the XY model isomorphic to the even 1-form-symmetry sector of the gauge theory. Consequently $D|\{S_1,\dots,S_n\}\rangle_{\pm}$ with $n$ even is an exact eigenstate of the gauge model at the same energy; the paper argues, from the tensor-network (PEPO) implementation of $D$, that these states retain area-law entanglement and therefore qualify as quantum many-body scars. The same construction is carried out for the honeycomb/triangular and kagome/dice lattices, and for part of the XXZ-type deformation.

Load-bearing premise

The load-bearing premise is that the tensor-network operator implementing the duality preserves area-law entanglement when applied to the stripe states; the paper asserts this from the operator's 'low-depth' character in Sec. 3.2 but supplies no proof and no direct computation of the dual states' entanglement entropies, so if the dual states in fact acquire volume-law entanglement they remain exact eigenstates yet cease to be quantum many-body scars in the standard sense.

Editorial extensions

If this is right

  • The dual $\mathbb{Z}_2$ gauge model acquires a tower of exact low-entanglement eigenstates at energies $2kh$ above the vacuum for $k$ up to $O(L)$ on the square lattice, placing scars squarely in the middle of a 2D gauge-theory spectrum.
  • The construction repeats for the triangular and dice lattice gauge models, so the mechanism is lattice-independent rather than a square-lattice accident.
  • Because the XY stripe states survive correlated disorder and inhomogeneous magnetic fields, the corresponding scars persist in disordered gauged models and can be given distinct energy labels for detection.
  • The XY model itself provides experimentally plausible hosts (Rydberg arrays, strongly interacting bosons in optical lattices, superconducting circuits) where the stripes could be prepared and their slow thermalization probed.
  • The gauging perspective suggests a general principle: gauging a subgroup of a global symmetry of a scarred model typically produces a scarred model, since gauging is implemented by a low-depth tensor network that preserves entanglement as long as the scars are not projected out.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The one open link is the entanglement claim for the dual states, and it is directly testable: computing the half-system entanglement entropy of $D|\{S_1,\dots,S_n\}\rangle$ on larger lattices would confirm the area law, or, if the entropy instead grows with subsystem volume, the states would remain exact eigenstates while losing the standard scar characterization.
  • A natural testable extension is to apply the same PEPO duality to other scarred lattice models with a $\mathbb{Z}_2$ symmetry — for instance the spin-1 XY model or the square-lattice Heisenberg scar candidates — and check whether their even-sector scars map to exact low-entanglement states of the corresponding gauge models.
  • The stripe mechanism is a 2D relative of the one-dimensional four-state construction, but with a key quantitative difference: the number of scar states grows with system size ($O(L)$ on the square lattice, exponentially on the kagome lattice), so the paper effectively constructs a scarred subspace whose dimension is large yet still exponentially smaller than the full Hilbert space.
  • Since the dual Hamiltonian sits at the critical point between trivial and SPT phases in the pivot-Hamiltonian family, the scar states live in a gapless gauge theory with a (2+1)-dimensional CFT limit; a dynamical probe, such as a quench starting from $D|S\rangle$, would test whether the scars produce the slow revivals characteristic of scar physics in an experimentally realisable gauge setting.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper constructs a family of exact energy eigenstates of the two-dimensional spin-1/2 XY model on tilted square, honeycomb, and kagome lattices, built from staggered superpositions of magnons along non-bending stripes or around hexagons. It proves, by direct commutator cancellation, that these states are exact eigenstates with zero XY energy, and it computes their entanglement entropies and identifies them as quantum many-body scars (QMBS). The paper then gauges the Z2 0-form symmetry through a Kramers-Wannier duality implemented as a PEPO, derives the intertwining relation D H_XY = H_dual D (Eq. 3.5), and maps even-number stripe states to exact eigenstates of the dual Z2 lattice-gauge model. The construction is extended to honeycomb/triangular and kagome/dice lattices, with an appendix treating the XXZ extension.

Significance. If the advertised claims hold, the paper provides rare examples of exact QMBS in two-dimensional spin and gauge models, with several strong technical assets: the algebraic proof in Appendix D is self-contained and parameter-free; the intertwining relation (3.5) is exact and clean; the disorder generalization and inhomogeneous-field bookkeeping are explicit; and the 12-site numerical entanglement spectra in Fig. 8 support the existence of low-entanglement eigenstates. The honeycomb/triangular construction appears to be a solid extension of the square-lattice mechanism. However, the paper's significance is reduced by a scope mismatch between the abstract and the body: the kagome/dice states are explicitly not QMBS in the homogeneous model by the paper's own criterion, and the 'middle of the spectrum' characterization for the square-lattice stripe states is not supported by the stated counting. These issues are fixable in revision, and I do not see a fatal flaw in the core algebraic derivation.

major comments (4)
  1. [Abstract; §5.1] The abstract's unconditional claim that 'the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual Z2 gauge model' is contradicted by §5.1, which explicitly states that the kagome hexagon states are ground states in fixed down-spin sectors and that 'interpreting these eigenstates as QMBS is not appropriate, since their energies are no longer located in the middle of the spectrum.' Section 5.2 only establishes that the dual dice-lattice states are exact eigenstates when the number of excitations is even. The advertised claim should be restricted to the square and honeycomb/triangular constructions, with the kagome/dice results presented as exact-eigenstate candidates rather than established QMBS.
  2. [§5.2] The proposed promotion of the kagome/dice states to QMBS by inhomogeneous magnetic fields is not carried out. The text says that 'these states can be promoted to QMBS by adding inhomogeneous magnetic fields designed to shift their energies,' but no explicit dice-lattice Hamiltonian with such fields is written, no proof is given that the corresponding dual fields preserve the eigenstate property under the duality operator, and no energy-shift calculation is supplied. Until this construction is provided, the claim that the dual dice-lattice states are QMBS remains unsupported.
  3. [§2.2] The statement at the end of §2.2 that the stripe states 'reside in the middle of the energy spectrum' does not follow from the preceding counting. For N = 2L^2 sites and k = O(L) stripes, the energy is E = h(2k - N) = -hN + O(L), so E/N → -h as L → ∞. Since the full Hamiltonian is invariant under the global spin flip that sends H_Z to -H_Z, the spectral center is near E = 0, making these states near the bottom of the spectrum rather than in the middle. This point is load-bearing for the QMBS identification, and the manuscript should either revise the energy-location argument or clarify which definition of 'middle of the spectrum' is being used.
  4. [§3.2] The assertion that the PEPO realization of the duality operator 'guarantees that it preserves the area-law scaling of entanglement entropy' is made without proof. This is not a fatal gap: the duality operator in Eq. (3.3) is a fixed-bond-dimension tensor network, and applying it to the stripe states, whose entanglement across any cut is controlled by the stripe-crossing fraction, should preserve area-law scaling. However, the paper should spell out this argument explicitly and, ideally, verify it by a direct computation of the entanglement entropy of D|S> for a small system, rather than relying on the ambiguous phrase 'low-depth tensor network operator.'
minor comments (4)
  1. [Appendix C] In Eq. (C.1), the fourth scar creation operator is written as Q±_{H3} twice; from the subsequent energy expressions it should be Q±_{V3}.
  2. [§2.3] In the paragraph following Eq. (2.19), the sentence defining N^{(A)}_{S_n} repeats 'N^{(A)}_{S_n}' twice; the second occurrence should presumably be N^{(B)}_{S_n}.
  3. [References] References [59] and [82] are the same paper (Lootens, Delcamp, Ortiz, Verstraete, PRX Quantum 4, 020357), and references [70] and [96] are the same arXiv preprint (arXiv:2501.12514); these duplicates should be consolidated.
  4. [§3.2] The phrase 'low-depth tensor network operator' is not defined in the text; since the PEPO in Eq. (3.3) is a fixed-bond-dimension tensor network, describing it in those terms rather than as a circuit would be clearer and would avoid implying a finite-depth unitary implementation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stripe eigenstates and their dual images follow from direct commutator identities and an operator intertwining relation, not from fitted inputs or self-citation.

full rationale

I find no circular step. The exact stripe eigenstates of the XY model are derived by an explicit commutator calculation (Eqs. 2.13-2.14): the hopping terms cancel pairwise because of the staggered sign choice, and the total energy is set by the U(1) magnetic-field term. Multiple-stripe states are obtained by applying commuting creation operators, and the energy eigenvalues are computed from H_Z, not fitted. The random disorder and inhomogeneous magnetic fields are introduced after the construction to split degeneracies and to allow numerical identification; they are not used to adjust the spectral position or entanglement of the scar states. The dual gauge model is not defined by demanding that D|S> be eigenstates; it is the image of the full XY Hamiltonian under the Kramers-Wannier/PEPO duality, and the relation D H_XY = H_double D (Eq. 3.5) is an operator identity. Therefore, if |S> is an eigenstate of H_XY with energy E, then D|S> is an eigenstate of H_double with the same energy, by direct substitution. The only questionable step is the unproven assertion in Sec. 3.2 that the PEPO is a low-depth tensor network operator preserving area-law entanglement; that is a missing proof or a correctness concern, not a circular argument. Self-citations such as [13] for the entanglement-entropy formula and [83] for the Bilinear Phase Map form are used for standard repackaging and are not load-bearing. The abstract's general claim about the kagome/dice case is in tension with Sec. 5.1's explicit caveat that the hexagon eigenstates are not in the middle of the spectrum and hence are not appropriately called QMBS, but this is a scope/overclaim issue, not circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central construction rests on a set of carefully chosen conditions (straight stripes, correlated disorder, thick stripes on honeycomb) and on an unproved structural assumption about the PEPO duality operator. No free parameters are fitted to data; the random couplings and fields are illustrative rather than fitted. No new physical entities are introduced.

assumptions (5)
  • ad hoc to paper Only straight, non-bending stripes yield exact eigenstates; bending stripes break the cancellation.
    Sec. 2.2 and Fig. 5: the construction excludes bending stripes, restricting the set of scar states.
  • ad hoc to paper The correlated disorder couplings satisfy recursion (2.24) and boundary condition (2.25).
    Appendix D: these conditions are imposed so that [H_XY, Q^+_S]|down> = 0; they are not physical constraints.
  • ad hoc to paper The duality operator D is a low-depth PEPO preserving area-law entanglement.
    Sec. 3.2: this unproved property is the basis for calling the dual states QMBS.
  • domain assumption The XY model in 2D has no nontrivial local conserved quantities, hence is non-integrable.
    Sec. 2.3, citing Ref. [28]: needed to exclude integrability as the reason for low-entanglement eigenstates.
  • ad hoc to paper On the honeycomb lattice, two sub-stripes must be combined into thick stripes with relative sign k = ±1 to complete cancellation.
    Sec. 4.1, Eqs. (4.2)-(4.3): the relative sign is a construction choice, not derived.

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Pith. "Pith review of Exact Quantum Many-Body Scars in 2D Quantum Gauge Models." pith.science (2026). https://pith.science/paper/I674IXJV

@misc{pith2026250521921,
  author       = {Pith},
  title        = {Pith review of: Exact Quantum Many-Body Scars in 2D Quantum Gauge Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I674IXJV}},
  note         = {Machine review of arXiv:2505.21921}
}
abstract

Quantum many-body scars (QMBS) serve as important examples of ergodicity-breaking phenomena in quantum many-body systems. Despite recent extensive studies, exact QMBS are rare in dimensions higher than one. In this paper, we study a two-dimensional quantum $\mathbb{Z}_2$ gauge model that is dual to a two-dimensional spin-$1/2$ XY model defined on bipartite graphs. We identify the exact eigenstates of the XY model with a tower structure as exact QMBS. Exploiting the duality transformation, we show that the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual $\mathbb{Z}_2$ gauge model. This construction is versatile and has potential applications for finding new QMBS in other higher-dimensional models.

Figures

Figures reproduced from arXiv: 2505.21921 by the authors.

Figure 1
Figure 1. Tilted square lattice where the XY model is defined. Spin- [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. We consider a staggered superposition of single up spin, taken from the stripe [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. When HXY moves around the up spin, the two contributions from nearby sites cancel out, thanks to the staggered choice of the relative signs in Eq. (2.10). This is a two-dimensional generalization of the one-dimensional counterpart shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: We can consider multiple stripes S, S′ , . . . , to obtain a collection of eigenstates. The number of such stripes can grow as O(L) for the linear system size L. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The cancelation mechanism fails when we have a bending strip. This means only straight stripes [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Demonstration of the entanglement entropy of the scar state with two excitations on stripes [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: The OBC lattice that we use to numerically calculate the entanglement entropy in Fig. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Entanglement entropy v.s. energy for the XY model with correlated interaction strengths and [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The entanglement entropies of the eigenstates of the XY model without the inhomogeneous [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: A schematic of the dual lattice-gauge Hamiltonian ( [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: A demonstration of the full PEPO acting on the XY spins through the green legs and obtaining [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: When HXY moves around the magnon excitations, the two contributions from nearby sites partially cancel out, but not completely [PITH_FULL_IMAGE:figures/full_fig_p020_12.png]
Figure 13
Figure 13. Figure 13: To complete the cancelation, we need another copy of the stripe and combine the two into a [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]
Figure 14
Figure 14. Figure 14: In addition to the stripe in Fig [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: We obtain an eigenstate from multiple stripes as long as the stripes are separated by at least two [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]
Figure 16
Figure 16. Figure 16: The kagome lattice, where we define the XY model. Periodic boundary condition are imposed. [PITH_FULL_IMAGE:figures/full_fig_p025_16.png]
Figure 17
Figure 17. Figure 17: A schematic of the dual lattice-gauge Hamiltonian ( [PITH_FULL_IMAGE:figures/full_fig_p026_17.png]
Figure 18
Figure 18. Figure 18: The magnons are excited at every other site of the one-dimensional spin chain, with a relative [PITH_FULL_IMAGE:figures/full_fig_p028_18.png]
Figure 19
Figure 19. Figure 19: The Hamiltonian moves a magnon to a neighboring site. There is, however, always a cancelation [PITH_FULL_IMAGE:figures/full_fig_p029_19.png]

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Works this paper leans on

101 extracted references · 21 canonical work pages

  1. [1]

    Quantum statistical mechanics in a closed system,

    J. M. Deutsch, “Quantum statistical mechanics in a closed system,”Phys. Rev. A43(Feb, 1991) 2046–2049.https://link.aps.org/doi/10.1103/PhysRevA.43.2046

    doi:10.1103/physreva.43.2046 1991

  2. [2]

    Chaos and quantum thermalization,

    M. Srednicki, “Chaos and quantum thermalization,”Phys. Rev. E50(Aug, 1994) 888–901. https://link.aps.org/doi/10.1103/PhysRevE.50.888

    doi:10.1103/physreve.50.888 1994

  3. [3]

    Proof of the ergodic theorem and the H-theorem in quantum mechanics,

    J. von Neumann, “Proof of the ergodic theorem and the H-theorem in quantum mechanics,”Eur. Phys. J. H35no. 2, (2010) 201–237.https://doi.org/10.1140/epjh/e2010-00008-5. [English translation of (by R. Tumulka) Z. Phys.57, 30 (1929)]

    work page doi:10.1140/epjh/e2010-00008-5 2010

  4. [4]

    From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,”Adv. Phys.65no. 3, (2016) 239–362, arXiv:1509.06411 [cond-mat.stat-mech]

    arXiv 2016

  5. [5]

    Weak ergodicity breaking from quantum many-body scars,

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, “Weak ergodicity breaking from quantum many-body scars,”Nature Physics14no. 7, (May, 2018) 745–749. http://dx.doi.org/10.1038/s41567-018-0137-5

    doi:10.1038/s41567-018-0137-5 2018

  6. [6]

    Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations,

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, “Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations,”Physical Review B98no. 15, (Oct., 2018) 155134. http://dx.doi.org/10.1103/PhysRevB.98.155134

    doi:10.1103/physrevb.98.155134 2018

  7. [7]

    Quantum many-body scars and weak breaking of ergodicity,

    M. Serbyn, D. A. Abanin, and Z. Papi´ c, “Quantum many-body scars and weak breaking of ergodicity,”Nature Phys.17no. 6, (2021) 675–685,arXiv:2011.09486 [quant-ph]

    arXiv 2021

  8. [8]

    Quantum many-body scars and Hilbert space fragmentation: a review of exact results,

    S. Moudgalya, B. A. Bernevig, and N. Regnault, “Quantum many-body scars and Hilbert space fragmentation: a review of exact results,”Rept. Prog. Phys.85no. 8, (2022) 086501, arXiv:2109.00548 [cond-mat.str-el]

    arXiv 2022

Show all 101 references
  1. [9]

    Quantum Many-Body Scars: A Quasiparticle Perspective,

    A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, “Quantum Many-Body Scars: A Quasiparticle Perspective,”Annu. Rev. Condens. Matter Phys.14no. 1, (2023) 443–469, arXiv:2206.11528 [cond-mat.str-el]. https://doi.org/10.1146/annurev-conmatphys-031620-101617

    2023 arXiv

  2. [10]

    Flat band quantum scar,

    Y. Kuno, T. Mizoguchi, and Y. Hatsugai, “Flat band quantum scar,”Physical Review B102no. 24, (Dec., 2020) 241115.http://dx.doi.org/10.1103/PhysRevB.102.241115

    2020 doi

  3. [11]

    Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field,

    A. Yoshinaga, H. Hakoshima, T. Imoto, Y. Matsuzaki, and R. Hamazaki, “Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field,”Phys. Rev. Lett.129no. 9, (2022) 090602,arXiv:2111.05586 [cond-mat.stat-mech]

    2022 arXiv

  4. [12]

    Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets,

    M. Schecter and T. Iadecola, “Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets,”Phys. Rev. Lett.123no. 14, (2019) 147201,arXiv:1906.10131 [cond-mat.str-el]. 33

    2019 arXiv

  5. [13]

    Quantum many-body scars in spin models with multibody interactions,

    K. Sanada, Y. Miao, and H. Katsura, “Quantum many-body scars in spin models with multibody interactions,”Phys. Rev. B108no. 15, (2023) 155102,arXiv:2304.13624 [cond-mat.str-el]

    2023 arXiv

  6. [14]

    Towers of Quantum Many-body Scars from Integrable Boundary States,

    K. Sanada, Y. Miao, and H. Katsura, “Towers of Quantum Many-body Scars from Integrable Boundary States,”arXiv:2411.01270 [cond-mat.stat-mech]

  7. [15]

    Quantum many-body scar states in two-dimensional Rydberg atom arrays,

    C.-J. Lin, V. Calvera, and T. H. Hsieh, “Quantum many-body scar states in two-dimensional Rydberg atom arrays,”Phys. Rev. B101(Jun, 2020) 220304. https://link.aps.org/doi/10.1103/PhysRevB.101.220304

    2020 doi

  8. [16]

    Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions,

    K. Tamura and H. Katsura, “Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions,”Phys. Rev. B106no. 14, (2022) 144306,arXiv:2207.06040 [quant-ph].https://doi.org/10.1103/PhysRevB.106.144306

    2022 arXiv

  9. [17]

    Scars from protected zero modes and beyond inU(1) quantum link and quantum dimer models,

    S. Biswas, D. Banerjee, and A. Sen, “Scars from protected zero modes and beyond inU(1) quantum link and quantum dimer models,”SciPost Phys.12no. 5, (2022) 148,arXiv:2202.03451 [cond-mat.str-el].https://www.scipost.org/SciPostPhys.12.5.148

    2022 arXiv

  10. [18]

    Quantum Many-Body Scarring in 2 + 1D Gauge Theories with Dynamical Matter,

    J. Osborne, I. P. McCulloch, and J. C. Halimeh, “Quantum Many-Body Scarring in 2 + 1D Gauge Theories with Dynamical Matter,”arXiv:2403.08858 [cond-mat.quant-gas]

    arXiv

  11. [19]

    Stabilizer Scars,

    J. Hartse, L. Fidkowski, and N. Mueller, “Stabilizer Scars,”arXiv:2411.12797 [quant-ph]

  12. [20]

    Disorder-free localization and many-body quantum scars from magnetic frustration,

    P. A. McClarty, M. Haque, A. Sen, and J. Richter, “Disorder-free localization and many-body quantum scars from magnetic frustration,”Phys. Rev. B102no. 22, (2020) 224303, arXiv:2007.01311 [cond-mat.stat-mech].https://doi.org/10.1103/PhysRevB.102.224303

    2020 arXiv

  13. [21]

    Exact Valence-Bond Solid Scars in the Square-Lattice Heisenberg Model,

    D. D. Dai, “Exact Valence-Bond Solid Scars in the Square-Lattice Heisenberg Model,” arXiv:2412.08874 [cond-mat.str-el]

    arXiv

  14. [22]

    The Bond-Algebraic Approach to Dualities,

    E. Cobanera, G. Ortiz, and Z. Nussinov, “The Bond-Algebraic Approach to Dualities,”Adv. Phys.60 (2011) 679–798,arXiv:1103.2776 [cond-mat.stat-mech]

    2011 arXiv

  15. [23]

    An introduction to lattice gauge theory and spin systems,

    J. B. Kogut, “An introduction to lattice gauge theory and spin systems,”Rev. Mod. Phys.51(Oct,

  16. [24]

    Ferromagnetism in the Hubbard model with topological/non-topological flat bands,

    H. Katsura, I. Maruyama, A. Tanaka, and H. Tasaki, “Ferromagnetism in the Hubbard model with topological/non-topological flat bands,”Europhys. Lett.91no. 5, (2010) 57007,arXiv:0907.4564 [cond-mat.str-el].https://dx.doi.org/10.1209/0295-5075/91/57007

    2010 arXiv

  17. [25]

    Generalized spin helix states in quantum spin graphs,

    C. H. Zhang, Y. B. Shi, and Z. Song, “Generalized spin helix states in quantum spin graphs,”Phys. Scripta100no. 3, (2025) 035912,arXiv:2310.11786 [quant-ph]

    2025 arXiv

  18. [26]

    All product eigenstates in Heisenberg models from a graphical construction,

    F. Gerken, I. Runkel, C. Schweigert, and T. Posske, “All product eigenstates in Heisenberg models from a graphical construction,”Phys. Rev. Res.7no. 1, (2025) L012008,arXiv:2310.13158 [cond-mat.str-el]

    2025 arXiv

  19. [27]

    Exact volume-law entangled zero-energy eigenstates in a large class of spin models,

    S. Mohapatra, S. Moudgalya, and A. C. Balram, “Exact volume-law entangled zero-energy eigenstates in a large class of spin models,”Phys. Rev. Lett.134no. 21, (2025) 210403,arXiv:2410.22773 [cond-mat.str-el].https://doi.org/10.1103/PhysRevLett.134.210403

    2025 arXiv

  20. [28]

    TheS= 1 2 XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities,

    N. Shiraishi and H. Tasaki, “TheS= 1 2 XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities,”arXiv:2412.18504 [cond-mat.stat-mech]

    arXiv

  21. [29]

    Kramers-wannier duality from conformal defects,

    J. Fr¨ ohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Kramers-wannier duality from conformal defects,”Phys. Rev. Lett.93(Aug, 2004) 070601. https://link.aps.org/doi/10.1103/PhysRevLett.93.070601

    2004 doi

  22. [30]

    Duality and defects in rational conformal field theory,

    J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Duality and defects in rational conformal field theory,”Nucl. Phys. B763(2007) 354–430,arXiv:hep-th/0607247. 34

    2007 arXiv

  23. [31]

    On finite symmetries and their gauging in two dimensions,

    L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions,”JHEP 03(2018) 189,arXiv:1704.02330 [hep-th]

    2018 arXiv

  24. [32]

    Topological Defects on the Lattice I: The Ising model,

    D. Aasen, R. S. K. Mong, and P. Fendley, “Topological Defects on the Lattice I: The Ising model,”J. Phys. A49no. 35, (2016) 354001,arXiv:1601.07185 [cond-mat.stat-mech]

    2016 arXiv

  25. [33]

    Topological Defects on the Lattice: Dualities and Degeneracies,

    D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,”arXiv:2008.08598 [cond-mat.stat-mech]

    2008 arXiv

  26. [34]

    Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry,

    L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry,”Phys. Rev. Res.2(Oct, 2020) 043086.https://link.aps.org/doi/10.1103/PhysRevResearch.2.043086

    2020 doi

  27. [35]

    Classification of topological phases with finite internal symmetries in all dimensions,

    L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Classification of topological phases with finite internal symmetries in all dimensions,”JHEP09(2020) 093,arXiv:2003.08898 [math-ph]

    2020 arXiv

  28. [36]

    Defect lines, dualities, and generalised orbifolds,

    J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Defect lines, dualities, and generalised orbifolds,” in16th International Congress on Mathematical Physics. 9, 2009.arXiv:0909.5013 [math-ph]

    2009 arXiv

  29. [37]

    Kramers-wannier-like duality defects in (3 + 1)dgauge theories,

    J. Kaidi, K. Ohmori, and Y. Zheng, “Kramers-wannier-like duality defects in (3 + 1)dgauge theories,” Phys. Rev. Lett.128(Mar, 2022) 111601. https://link.aps.org/doi/10.1103/PhysRevLett.128.111601

    2022 doi

  30. [38]

    Symmetry TFTs for Non-invertible Defects,

    J. Kaidi, K. Ohmori, and Y. Zheng, “Symmetry TFTs for Non-invertible Defects,”Commun. Math. Phys.404no. 2, (2023) 1021–1124,arXiv:2209.11062 [hep-th]

    2023 arXiv

  31. [39]

    Non-invertible symmetries ofN= 4 SYM and twisted compactification,

    J. Kaidi, G. Zafrir, and Y. Zheng, “Non-invertible symmetries ofN= 4 SYM and twisted compactification,”JHEP08(2022) 053,arXiv:2205.01104 [hep-th]

    2022 arXiv

  32. [40]

    Fermionic minimal models,

    C.-T. Hsieh, Y. Nakayama, and Y. Tachikawa, “Fermionic minimal models,”Phys. Rev. Lett.126 (May, 2021) 195701.https://link.aps.org/doi/10.1103/PhysRevLett.126.195701

    2021 doi

  33. [41]

    Open spin chain realization of a topological defect in a one-dimensional ising model: Boundary and bulk symmetry,

    Y. Fukusumi and S. Iino, “Open spin chain realization of a topological defect in a one-dimensional ising model: Boundary and bulk symmetry,”Phys. Rev. B104(Sep, 2021) 125418. https://link.aps.org/doi/10.1103/PhysRevB.104.125418

    2021 doi

  34. [42]

    Fermionization and boundary states in 1+1 dimensions,

    Y. Fukusumi, Y. Tachikawa, and Y. Zheng, “Fermionization and boundary states in 1+1 dimensions,” SciPost Phys.11(2021) 082.https://scipost.org/10.21468/SciPostPhys.11.4.082

    2021 doi

  35. [43]

    Topological Defect Lines in Two Dimensional Fermionic CFTs,

    C.-M. Chang, J. Chen, and F. Xu, “Topological Defect Lines in Two Dimensional Fermionic CFTs,” SciPost Phys.15(2023) 216,arXiv:2208.02757 [hep-th]

    2023 arXiv

  36. [44]

    Topological holography: Towards a unification of Landau and beyond-Landau physics,

    H. Moradi, S. F. Moosavian, and A. Tiwari, “Topological holography: Towards a unification of Landau and beyond-Landau physics,”SciPost Phys. Core6(2023) 066,arXiv:2207.10712 [cond-mat.str-el]

    2023 arXiv

  37. [45]

    Non-invertible higher-categorical symmetries,

    L. Bhardwaj, L. E. Bottini, S. Schafer-Nameki, and A. Tiwari, “Non-invertible higher-categorical symmetries,”SciPost Phys.14no. 1, (2023) 007,arXiv:2204.06564 [hep-th]

    2023 arXiv

  38. [46]

    Universal Non-Invertible Symmetries,

    L. Bhardwaj, S. Schafer-Nameki, and J. Wu, “Universal Non-Invertible Symmetries,”Fortsch. Phys. 70no. 11, (2022) 2200143,arXiv:2208.05973 [hep-th]

    2022 arXiv

  39. [47]

    Non-invertible Symmetries and Higher Representation Theory I,

    T. Bartsch, M. Bullimore, A. E. V. Ferrari, and J. Pearson, “Non-invertible Symmetries and Higher Representation Theory I,”arXiv:2208.05993 [hep-th]

    arXiv

  40. [48]

    Unifying constructions of non-invertible symmetries,

    L. Bhardwaj, S. Schafer-Nameki, and A. Tiwari, “Unifying constructions of non-invertible symmetries,”SciPost Phys.15no. 3, (2023) 122,arXiv:2212.06159 [hep-th]

    2023 arXiv

  41. [49]

    Higher categorical symmetries and gauging in two-dimensional spin systems,

    C. Delcamp and A. Tiwari, “Higher categorical symmetries and gauging in two-dimensional spin systems,”SciPost Phys.16(2024) 110.https://scipost.org/10.21468/SciPostPhys.16.4.110. 35

    2024 doi

  42. [50]

    Categorical symmetry of the standard model from gravitational anomaly,

    P. Putrov and J. Wang, “Categorical symmetry of the standard model from gravitational anomaly,” Phys. Rev. D110(Dec, 2024) 125028.https://link.aps.org/doi/10.1103/PhysRevD.110.125028

    2024 doi

  43. [51]

    When are Duality Defects Group-Theoretical?,

    Z. Sun and Y. Zheng, “When are Duality Defects Group-Theoretical?,”arXiv:2307.14428 [hep-th]

    arXiv

  44. [52]

    Generalized symmetries in singularity-free nonlinear σmodels and their disordered phases,

    S. D. Pace, C. Zhu, A. Beaudry, and X.-G. Wen, “Generalized symmetries in singularity-free nonlinear σmodels and their disordered phases,”Phys. Rev. B110(Nov, 2024) 195149. https://link.aps.org/doi/10.1103/PhysRevB.110.195149

    2024 doi

  45. [53]

    Noninvertible symmetry-protected topological order in a group-based cluster state,

    C. Fechisin, N. Tantivasadakarn, and V. V. Albert, “Noninvertible symmetry-protected topological order in a group-based cluster state,”Phys. Rev. X15(Mar, 2025) 011058. https://link.aps.org/doi/10.1103/PhysRevX.15.011058

    2025 doi

  46. [54]

    Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model,

    M. Sinha, F. Yan, L. Grans-Samuelsson, A. Roy, and H. Saleur, “Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model,”JHEP07(2024) 225,arXiv:2310.19703 [hep-th]

    2024 arXiv

  47. [55]

    What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,

    S.-H. Shao, “What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,” arXiv:2308.00747 [hep-th]

    arXiv

  48. [56]

    Self-duality under gauging a non-invertible symmetry,

    Y. Choi, D.-C. Lu, and Z. Sun, “Self-duality under gauging a non-invertible symmetry,”JHEP01 (2024) 142,arXiv:2310.19867 [hep-th]

    2024 arXiv

  49. [57]

    Emergent generalized symmetries in ordered phases and applications to quantum disordering,

    S. D. Pace, “Emergent generalized symmetries in ordered phases and applications to quantum disordering,”SciPost Phys.17no. 3, (2024) 080,arXiv:2308.05730 [cond-mat.str-el]

    2024 arXiv

  50. [58]

    Fusion surface models: 2+1d lattice models from fusion 2-categories,

    K. Inamura and K. Ohmori, “Fusion surface models: 2+1d lattice models from fusion 2-categories,” SciPost Phys.16(2024) 143,arXiv:2305.05774 [cond-mat.str-el]

    2024 arXiv

  51. [59]

    Dualities in one-dimensional quantum lattice models: Symmetric hamiltonians and matrix product operator intertwiners,

    L. Lootens, C. Delcamp, G. Ortiz, and F. Verstraete, “Dualities in one-dimensional quantum lattice models: Symmetric hamiltonians and matrix product operator intertwiners,”PRX Quantum4(Jun,

  52. [60]

    Duality, criticality, anomaly, and topology in quantum spin-1 chains,

    H. Yang, L. Li, K. Okunishi, and H. Katsura, “Duality, criticality, anomaly, and topology in quantum spin-1 chains,”Phys. Rev. B107(Mar, 2023) 125158. https://link.aps.org/doi/10.1103/PhysRevB.107.125158

    2023 doi

  53. [61]

    Noninvertible duality transformation between symmetry-protected topological and spontaneous symmetry breaking phases,

    L. Li, M. Oshikawa, and Y. Zheng, “Noninvertible duality transformation between symmetry-protected topological and spontaneous symmetry breaking phases,”Phys. Rev. B108(Dec,

  54. [62]

    Subsystem non-invertible symmetry operators and defects,

    W. Cao, L. Li, M. Yamazaki, and Y. Zheng, “Subsystem non-invertible symmetry operators and defects,”SciPost Phys.15no. 4, (2023) 155,arXiv:2304.09886 [cond-mat.str-el]

    2023 arXiv

  55. [63]

    Intrinsically/purely gapless-SPT from non-invertible duality transformations,

    L. Li, M. Oshikawa, and Y. Zheng, “Intrinsically/purely gapless-SPT from non-invertible duality transformations,”SciPost Phys.18(2025) 153. https://scipost.org/10.21468/SciPostPhys.18.5.153

    2025 doi

  56. [64]

    214429.https://link.aps.org/doi/10.1103/PhysRevB.108.214429

    doi

  57. [65]

    Majorana chain and Ising model – (non-invertible) translations, anomalies, and emanant symmetries,

    N. Seiberg and S.-H. Shao, “Majorana chain and Ising model – (non-invertible) translations, anomalies, and emanant symmetries,”SciPost Phys.16(2024) 064,arXiv:2307.02534 [cond-mat.str-el]

    2024 arXiv

  58. [66]

    Generating lattice non-invertible symmetries,

    W. Cao, L. Li, and M. Yamazaki, “Generating lattice non-invertible symmetries,”SciPost Phys.17 no. 4, (2024) 104,arXiv:2406.05454 [cond-mat.str-el]

    2024 arXiv

  59. [67]

    Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space,

    N. Seiberg, S. Seifnashri, and S.-H. Shao, “Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space,”SciPost Phys.16(2024) 154,arXiv:2401.12281 [cond-mat.str-el]

    2024 arXiv

  60. [68]

    Noninvertible Symmetries Act Locally by Quantum Operations,

    M. Okada and Y. Tachikawa, “Noninvertible Symmetries Act Locally by Quantum Operations,”Phys. Rev. Lett.133(Nov, 2024) 191602.https://link.aps.org/doi/10.1103/PhysRevLett.133.191602

    2024 doi

  61. [69]

    Noninvertible Symmetry-Enriched Quantum Critical Point,

    L. Li, R.-Z. Huang, and W. Cao, “Noninvertible Symmetry-Enriched Quantum Critical Point,” arXiv:2411.19034 [cond-mat.str-el]

    arXiv

  62. [70]

    Realizing triality andp-ality by lattice twisted gauging in (1+1)d quantum spin systems,

    D.-C. Lu, Z. Sun, and Y.-Z. You, “Realizing triality andp-ality by lattice twisted gauging in (1+1)d quantum spin systems,”SciPost Phys.17(2024) 136. https://scipost.org/10.21468/SciPostPhys.17.5.136. 36

    2024 doi

  63. [71]

    Gauging non-invertible symmetries on the lattice,

    S. Seifnashri, S.-H. Shao, and X. Yang, “Gauging non-invertible symmetries on the lattice,” arXiv:2503.02925 [cond-mat.str-el]

    arXiv

  64. [72]

    Duality in Generalized Ising Models and Phase Transitions Without Local Order Parameters,

    F. J. Wegner, “Duality in Generalized Ising Models and Phase Transitions Without Local Order Parameters,”J. Math. Phys.12(1971) 2259–2272

    1971

  65. [74]

    Gauging quantum states: From global to local symmetries in many-body systems,

    J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, “Gauging quantum states: From global to local symmetries in many-body systems,”Phys. Rev. X5(Feb, 2015) 011024. https://link.aps.org/doi/10.1103/PhysRevX.5.011024

    2015 doi

  66. [75]

    Higher Gauging and Non-invertible Condensation Defects,

    K. Roumpedakis, S. Seifnashri, and S.-H. Shao, “Higher Gauging and Non-invertible Condensation Defects,”Commun. Math. Phys.401no. 3, (2023) 3043–3107,arXiv:2204.02407 [hep-th]

    2023 arXiv

  67. [76]

    Pivot Hamiltonians as generators of symmetry and entanglement,

    N. Tantivasadakarn, R. Thorngren, A. Vishwanath, and R. Verresen, “Pivot Hamiltonians as generators of symmetry and entanglement,”SciPost Phys.14no. 2, (2023) 012,arXiv:2110.07599 [cond-mat.str-el]

    2023 arXiv

  68. [77]

    Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup,

    L. Su and M. Zeng, “Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup,”Phys. Rev. B109(Jun, 2024) 245108. https://link.aps.org/doi/10.1103/PhysRevB.109.245108

    2024 doi

  69. [78]

    Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part II,

    L. Bhardwaj, S. Schafer-Nameki, A. Tiwari, and A. Warman, “Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part II,”arXiv:2502.20440 [hep-th]

    arXiv

  70. [79]

    Non-invertible and higher-form symmetries in 2+1d lattice gauge theories,

    Y. Choi, Y. Sanghavi, S.-H. Shao, and Y. Zheng, “Non-invertible and higher-form symmetries in 2+1d lattice gauge theories,”SciPost Phys.18(2025) 008. https://scipost.org/10.21468/SciPostPhys.18.1.008

    2025 doi

  71. [80]

    Building models of topological quantum criticality from pivot Hamiltonians,

    N. Tantivasadakarn, R. Thorngren, A. Vishwanath, and R. Verresen, “Building models of topological quantum criticality from pivot Hamiltonians,”SciPost Phys.14(2023) 013. https://scipost.org/10.21468/SciPostPhys.14.2.013

    2023 doi

  72. [81]

    Application of spin-wave theory to the ground state of xy quantum hamiltonians,

    G. Gomez-Santos and J. D. Joannopoulos, “Application of spin-wave theory to the ground state of xy quantum hamiltonians,”Phys. Rev. B36(Dec, 1987) 8707–8711. https://link.aps.org/doi/10.1103/PhysRevB.36.8707

    1987 doi

  73. [82]

    Duality viewpoint of noninvertible symmetry protected topological phases,

    W. Cao, M. Yamazaki, and L. Li, “Duality viewpoint of noninvertible symmetry protected topological phases,”arXiv:2502.20435 [cond-mat.str-el]

  74. [83]

    Generalized Kramers-Wanier Duality from Bilinear Phase Map,

    H. Yan and L. Li, “Generalized Kramers-Wanier Duality from Bilinear Phase Map,” arXiv:2403.16017 [cond-mat.str-el]

    arXiv

  75. [84]

    Exact solution of an ising model with three-spin interactions on a triangular lattice,

    R. J. Baxter and F. Y. Wu, “Exact solution of an ising model with three-spin interactions on a triangular lattice,”Phys. Rev. Lett.31(Nov, 1973) 1294–1297. https://link.aps.org/doi/10.1103/PhysRevLett.31.1294. 37

    1973 doi

  76. [85]

    Dualities in One-Dimensional Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners,

    L. Lootens, C. Delcamp, G. Ortiz, and F. Verstraete, “Dualities in One-Dimensional Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners,”PRX Quantum4 no. 2, (2023) 020357,arXiv:2112.09091 [quant-ph]

    2023 arXiv

  77. [86]

    Particle statistics, frustration, and ground-state energy,

    W. Nie, H. Katsura, and M. Oshikawa, “Particle statistics, frustration, and ground-state energy,” Phys. Rev. B97no. 12, (2018) 125153,arXiv:1401.2090 [cond-mat.stat-mech]. https://doi.org/10.1103/PhysRevB.97.125153

    2018 arXiv

  78. [87]

    Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices,

    J. Schulenburg, A. Honecker, J. Schnack, J. Richter, and H.-J. Schmidt, “Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices,”Phys. Rev. Lett.88no. 16, (2002) 167207,arXiv:cond-mat/0108498 [cond-mat.str-el]. https://doi.org/10.1103/Ph...

    2002 arXiv

  79. [88]

    Bose–Hubbard model on two-dimensional line graphs,

    J. Motruk and A. Mielke, “Bose–Hubbard model on two-dimensional line graphs,”J. Phys. A: Math. Theor.45no. 22, (2012) 225206,arXiv:1112.0131 [cond-mat.stat-mech]. https://iopscience.iop.org/article/10.1088/1751-8113/45/22/225206/meta

    2012 arXiv

  80. [89]

    Relaxation of an isolated dipolar-interacting Rydberg quantum spin system,

    A. P. Orioli, A. Signoles, H. Wildhagen, G. G¨ unter, J. Berges, S. Whitlock, and M. Weidem¨ uller, “Relaxation of an isolated dipolar-interacting Rydberg quantum spin system,”Phys. Rev. Lett.120 no. 6, (2018) 063601,arXiv:1703.05957 [physics.atom-ph]. https://doi.org/10.1103/...

    2018 arXiv

  81. [90]

    Glassy dynamics in a disordered Heisenberg quantum spin system,

    A. Signoles, T. Franz, R. Ferracini Alves, M. G¨ arttner, S. Whitlock, G. Z¨ urn, and M. Weidem¨ uller, “Glassy dynamics in a disordered Heisenberg quantum spin system,”Phys. Rev. X11no. 1, (2021) 011011,arXiv:1909.11959 [quant-ph].https://doi.org/10.1103/PhysRevX.11.011011

    2021 arXiv

  82. [91]

    Exact low-temperature behavior of a kagom´ e antiferromagnet at high fields,

    M. Zhitomirsky and H. Tsunetsugu, “Exact low-temperature behavior of a kagom´ e antiferromagnet at high fields,”Physical Review B—Condensed Matter and Materials Physics70no. 10, (2004) 100403, arXiv:cond-mat/0405578 [cond-mat.stat-mech]. https://doi.org/10.1103/PhysRevB.70.100403

    2004 arXiv

  83. [92]

    Continuous symmetry breaking in a two-dimensional Rydberg array,

    C. Chen, G. Bornet, M. Bintz, G. Emperauger, L. Leclerc, V. S. Liu, P. Scholl, D. Barredo, J. Hauschild, S. Chatterjee,et al., “Continuous symmetry breaking in a two-dimensional Rydberg array,”Nature616no. 7958, (2023) 691–695,arXiv:2207.12930 [cond-mat.quant-gas]. https://doi...

    2023 arXiv

  84. [93]

    A lattice model of liquid helium, I,

    T. Matsubara and H. Matsuda, “A lattice model of liquid helium, I,”Prog. Theor. Phys.16no. 6, (1956) 569–582.https://doi.org/10.1143/PTP.16.569

    1956 doi

  85. [94]

    Floquet Hamiltonian engineering of an isolated many-body spin system,

    S. Geier, N. Thaicharoen, C. Hainaut, T. Franz, A. Salzinger, A. Tebben, D. Grimshandl, G. Z¨ urn, and M. Weidem¨ uller, “Floquet Hamiltonian engineering of an isolated many-body spin system,” Science374no. 6571, (2021) 1149–1152,arXiv:2105.01597 [cond-mat.quant-gas]. https://...

    2021 arXiv

  86. [95]

    From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects,

    L. Eck and P. Fendley, “From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects,”SciPost Phys.16(2024) 127. https://scipost.org/10.21468/SciPostPhys.16.5.127

    2024 doi

  87. [96]

    Global symmetries of quantum lattice models under non-invertible dualities,

    W. Cao, Y. Miao, and M. Yamazaki, “Global symmetries of quantum lattice models under non-invertible dualities,”arXiv:2501.12514 [cond-mat.str-el]

  88. [97]

    Thermalization and criticality on an analogue–digital quantum simulator,

    T. I. Andersenet al., “Thermalization and criticality on an analogue–digital quantum simulator,” Nature638no. 8049, (2025) 79–85,arXiv:2405.17385 [quant-ph]

    2025 arXiv

  89. [98]

    Symmetry-protected topological phases from decorated domain walls,

    X. Chen, Y.-M. Lu, and A. Vishwanath, “Symmetry-protected topological phases from decorated domain walls,”Nature Commun.5no. 1, (2014) 3507

    2014

  90. [99]

    Decorated defect construction of gapless-SPT states,

    L. Li, M. Oshikawa, and Y. Zheng, “Decorated defect construction of gapless-SPT states,”SciPost Phys.17no. 1, (2024) 013,arXiv:2204.03131 [cond-mat.str-el]. 38

    2024 arXiv

  91. [100]

    Duality viewpoint of criticality,

    L. Li and Y. Yao, “Duality viewpoint of criticality,”Phys. Rev. B106no. 22, (2022) 224420, arXiv:2209.13450 [quant-ph]

    2022 arXiv

  92. [1979]

    659–713.https://link.aps.org/doi/10.1103/RevModPhys.51.659

    doi

  93. [2023]

    020357.https://link.aps.org/doi/10.1103/PRXQuantum.4.020357

    doi

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