Pith. sign in

REVIEW 3 major objections 5 minor 2 cited by

Constructing Quantum Many-Body Scars from Hilbert Space Fragmentation

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A kinetically constrained spin ladder can be engineered so that injecting a single quasiparticle into frozen clusters creates exact quantum many-body scars.

desk verdict A solid, honest construction of exact scars in a fragmented spin ladder, with a conjectural classification that the authors flag themselves; the exact Z6 tower is the cleanest result. read the letter →

arxiv 2506.10806 v2 pith:PGXYSWUO submitted 2025-06-12 quant-ph cond-mat.quant-gascond-mat.stat-mechphysics.atom-ph

Fan Yang , Matteo Magoni , Hannes Pichler This is my paper
classification quant-phcond-mat.quant-gascond-mat.stat-mechphysics.atom-ph
keywords quantummany-bodyscarsHilbertspacefragmentationkineticallyconstrainedspinladderweakergodicitybreakinghard-corebosonmappingneutral-atomsimulatorsLindbladmasterequationRydberginteractions
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

This paper aims to show that quantum many-body scars—states that refuse to thermalize inside an otherwise thermalizing system—can be built systematically from Hilbert space fragmentation, rather than discovered one model at a time. In a kinetically constrained spin ladder, the authors identify frozen cluster regions and mobile string defects, and argue that a short string injected into a staggered frozen background acts as a single quasiparticle whose motion generates an exact, closed scar space. For chain lengths $L = 6k - 1$, the scar space is spanned by powers of a raising operator acting on a root state, which is equivalent to one hard-core boson hopping on a chain, with area-law entanglement despite sitting in the middle of the spectrum. Two quasiparticles collide inelastically and leak into the thermal sector at a rate the authors describe as two-body loss in a Lindblad master equation, yielding approximate scars. If correct, this gives a scalable recipe for exact and approximate scars with genuine spatial connectivity, and it maps directly onto neutral-atom Rydberg simulators.

What carries the argument

The central machinery is the decomposition of product states into frozen clusters (domains of $p \ge 3$ consecutive identical spins) and mobile strings (sequences of $l$ identical spins separated by gaps), together with the four string–cluster scattering rules (i)–(iv). In particular, rule (iii) states that a free string of length $l \le 2$ fully activates a cluster of size $p \le 4$ but only partially activates a cluster of size $p \ge 5$, while rule (iv) states that a string of length $l \ge 3$ fully activates clusters of any size. These rules determine which Krylov subspace (the set of states reachable from a root state by repeated Hamiltonian action) a root state generates: suppressing long strings keeps the dynamics inside a polynomially large scar space. The exact tower is generated by rewriting the intra-chain hopping as $H^{[2]} = J_+ + J_-$, where $J_+$ raises a magnon–hole pair; for $L = 6k-1$ the repeated action of $J_+$ on $|\psi_1\rangle$ closes into $K_s$, and the map $(J_+)^n |\psi_1\rangle \leftrightarrow c^\dagger_n |0\rangle$ turns the scar dynamics into a free hard-core boson tight-binding chain.

What would settle it

Exactly diagonalize the symmetry sector $\{N_I = N_{II} = (L+3)/2\}$ for $L = 23$ and check whether every state $(J_+)^n |\psi_1\rangle$ stays inside the proposed closed scar space $K_s$; any nonzero matrix element connecting $K_s$ to the thermal subsector $K_t$ would falsify the exact-scar construction. For the approximate scars, initialize the two-quasiparticle root state $|\psi_2\rangle$ and compare the measured scar-space population to the two-body-loss Lindblad prediction of Eq. (6), including the non-Markovian pseudo-mode refinement; a systematic discrepancy that persists as $L$ grows would falsify the effective-loss description.

Watch

Extended reading notes

Core claim

The central claim is that weak Hilbert space fragmentation in this kinetically constrained spin ladder is generated by strings that only partially activate frozen clusters, and that this mechanism yields a systematic construction of quantum many-body scars. For chain lengths $L = 6k - 1$ ($k = 2,3,\ldots$), the root state $|\psi_1\rangle$—a staggered pattern of clusters carrying one attached magnon—generates a closed scar space $K_s = \mathrm{span}\{|\psi_1\rangle, J_+|\psi_1\rangle, \ldots, (J_+)^M|\psi_1\rangle\}$ with $M = (L-2)/3$, and the scar-space dynamics is exactly a single hard-core boson hopping on a chain. These eigenstates show area-law entanglement while sitting in the middle of the spectrum, and the remainder of their symmetry sector is a nonintegrable thermal subsector with Wigner-Dyson level statistics. Injecting two quasiparticles produces an $O(L^2)$ subspace of approximate scars whose leakage to the thermal sector is governed by an emergent two-body loss, described quantitatively by a Lindblad master equation and improved with a small set of pseudo-modes.

Load-bearing premise

The load-bearing premise is that a short string (a mobile run of one or two identical spins) can only partially activate a frozen cluster of five or more spins, so that the long strings that fully activate the system are never created in the scar subspace; this rule is checked numerically only up to $L=22$, and its validity for all sizes is a conjecture.

Editorial extensions

If this is right

  • For $L = 6k-1$, the model hosts a tower of exact quantum many-body scars whose dimension grows linearly with system size, so the construction is scalable rather than an artifact of small chains.
  • The scar-space Hamiltonian is exactly a noninteracting tight-binding chain, so the scar dynamics, revivals, and entanglement can be computed from a single-particle picture even though the scars lie mid-spectrum.
  • Quenches from the root state $|\psi_1\rangle$ should show persistent non-thermal revivals, because the scar subspace is dynamically disconnected from the thermal subsector.
  • In the two-quasiparticle sector, the inelastic collision produces approximate scars that decay through a two-body loss channel, and increasing the interaction $V_3$ suppresses the leakage.
  • The Hamiltonian and constraints can be realized in neutral-atom Rydberg simulators, where strong Rydberg interactions give the required $V \gg J$ regime and stroboscopic dressing provides long-lived dynamics.

Reading between the lines

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

  • If the string–cluster rules hold beyond $L=22$, the same short-string-into-frozen-cluster recipe should transfer to other kinetically constrained lattices, including two-dimensional arrays, where the quasiparticle picture would need only a generalized notion of string.
  • The emergent two-body loss could be used as an engineered dissipation channel: tuning $V_3$ and the hopping ratio may allow dissipative preparation of entangled quasiparticle pairs or scar-space populations, a control strategy the paper sketches but does not develop.
  • The contrast between elastic collisions (strong fragmentation) and inelastic collisions (weak fragmentation) suggests a diagnostic: systems whose quasiparticles only scatter elastically are unlikely to exhibit the approximate-scar phenomenology described here.
  • The many-body-caging zero mode identified in the two-quasiparticle sector invites a stability test: adding perturbations that break the kinetic constraints should reveal whether the zero mode survives as a localized dynamical feature.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper studies a spin-1/2 anisotropic Heisenberg model on a triangular ladder in the strong-Ising regime V >> J, where the effective Hamiltonian (2) conserves both magnon number N_I and magnon-bond number N_II. The authors show that the constrained Hilbert space fragments into a primary thermal Krylov subspace and an exponentially large set of small Krylov subspaces, and they propose a bottom-up construction of quantum many-body scars (QMBS) by injecting short strings into frozen cluster patterns. For root states built on staggered clusters |Z_{2p}>, an injected length-2 string yields scar spaces of dimension ~L or ~L^2; for the special |Z_6> root state and L = 6k-1, they obtain a closed scar tower K_s = span{|psi1>, J+|psi1>, ..., (J+)^M|psi1>} with M = (L-2)/3, equivalent to hard-core boson hopping. They also study two-quasiparticle inelastic collisions, modeling the leakage to the thermal space as a two-body loss described by a Lindblad master equation (Eq. (6)) or by a pseudo-mode non-Markovian model. Numerical evidence is provided from entanglement entropy, level statistics, and scar-space populations. The exactness of the scar tower relies on string-cluster scattering rules (i)-(iv) that are illustrated by small examples and verified up to L=22, but not proven for arbitrary sizes; the long-string rule is explicitly conjectural. The approximate-scar validation uses parameters extracted or fitted from the same exact correlation function it is meant to reproduce.

Significance. If the closure rules are proven, the paper would provide a minimal, experimentally realizable (neutral-atom/Rydberg) model that unifies weak Hilbert space fragmentation with exact and approximate QMBS, including a parameter-free exact tower with area-law entanglement in the middle of the spectrum and a Wigner-Dyson thermal sector. The string-cluster interpretation is intuitive and the open-system reformulation in terms of emergent two-body loss is a useful conceptual tool. The manuscript also includes transparent sector-dimension recurrences in the Supplemental Material and explicit connectivity graphs. However, the central exactness claim is conditional on conjectural scattering rules, and the quantitative agreement of the approximate-scar model is partly a fit to the exact dynamics. The paper's value is high if the missing algebraic proofs are supplied and the predictive content of the open-system model is clarified.

major comments (3)
  1. [Construction of exact scars; SM Sec. III] The closure of the scar space for the Z6 tower is not established at arbitrary system size. The statement after Eq. (4) that K_s = span{|psi1>, J+|psi1>, ..., (J+)^M|psi1>} is closed under H[1] and generated by H[2] relies on the string-cluster rules (i)-(iv) stated after Fig. 2 and detailed in SM Sec. III. Rule (iii), which asserts that a free string with l <= 2 can only partially activate a p >= 5 cluster, is central: if a short string could fully activate a p >= 5 cluster, states in K_s would leak into the thermal subsector. These rules are supported by selected examples and by numerics up to L=22, but they are not derived for arbitrary cluster sizes or separations, and the complementary statement for long strings is explicitly conjectural in SM Sec. III ("we conjecture that a free long string with l >= 3 can always generate a primary Krylov subsector approaching the size of the given symmetry sector up to the thermodynamic limit"). Please provide a proof of the closure of K_s and of the scattering rules for arbitrary p and l, or explicitly present the exact scar construction as a conjecture with the finite-size evidence as its support.
  2. [SM Sec. IV; Eq. (6); Fig. 3(c)] The validation of the open-system description is partly circular. In the Markovian master equation (6), the damping rates Gamma_n and the Lamb shifts delta V_n are extracted from the numerically exact reservoir correlation function G_nn(t) (SM Eq. (S10)), and in the pseudo-mode model the parameters Delta_{sigma,n}, lambda_{sigma,n}, kappa_{sigma,n} are fitted to the same G_nn(t) via SM Eq. (S14). The dashed and solid curves in Fig. 3(c) therefore reproduce the exact dynamics with parameters obtained from that exact dynamics, rather than providing an independent prediction. Please clarify which observables are genuine predictions of the model, quantify the sensitivity of the results to the fitted parameters, and test the model on data not used in the fit (e.g., different initial separations or interaction strengths V3). Without such a test, the agreement in Fig. 3(c) supports the model as a useful parameterization but not as an emergent two-body-loss prediction.
  3. [Construction of approximate scars; SM Sec. V] The claim that the two-quasiparticle elastic-collision sector forms an O(L^2) scar space with O(L) couplings to the thermal space is not proven. The mapping sigma^x_{3n+1}(J^-)^{N-m} sigma^x_{3n+1}(J^+)^n |psi2> <-> c^dagger_m c^dagger_n |0> is stated after Eq. (5) without a derivation that the image states are orthogonal, that they span an invariant subspace under H[1] and H[2], or that leakage is restricted to a set of O(L) boundary terms. The approximate-scar interpretation in SM Sec. V relies on exactly these properties. Please supply the construction of the mapping, the invariance argument (or numerical evidence for the leakage scaling with L), and an explicit expression for the leakage Hamiltonian.
minor comments (5)
  1. [Model; Eqs. (3)-(5)] The root states are defined only via inline pictorial notation that does not render in the text version; please provide explicit spin configurations in terms of |--> and |o> (or a supplementary figure) so that the constructions are legible and reproducible.
  2. [SM Sec. II] The recurrence relations in Eq. (S3) are stated without their boundary conditions; please include the boundary conditions so the reader can reproduce the dimension counting.
  3. [SM Sec. IV] The statement that the off-diagonal correlators G_{mn}(t)|_{m != n} is approximately zero and that G_nn(t) converges with system size is not accompanied by data; please show the finite-size convergence or give the system sizes used.
  4. [SM Sec. V] The zero-energy eigenstate |zero> in Eq. (S15) is presented without verification; briefly demonstrate that H_eff |zero> = 0 or state that it is checked numerically.
  5. [Figs. 1(c) and 3(b)] The entanglement-entropy panel and the correlation-function panel lack axis labels and scales in the text version; please ensure all panels have labeled axes and legends.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the exact scar tower is a self-contained Krylov-space construction, and the approximate-scar master equation is parameterized by reservoir correlation functions rather than by the population it is compared with.

full rationale

The central exact scar construction is self-contained and parameter-free: from the constrained Hamiltonian H_eff in Eq. (2), the paper defines strings and clusters, chooses root states, and builds the scar tower Ks as the Krylov subspace generated by H[2] from |ψ1⟩. The mapping to a hard-core boson hopping chain is a relabeling of that Krylov tower, not an independent prediction fitted to data; the nontrivial content is the claimed closure of the tower, which is a mathematical statement about the fixed microscopic Hamiltonian, not an input assumed into the result. The approximate-scar analysis is also not a fitted-input-called-prediction: in Eq. (6), the Markovian rates Γn and Lamb shifts δVn are extracted from the reservoir autocorrelation function Gnn(t) (SM Eq. S10), and the pseudo-mode parameters are fitted to Gnn(t) (SM Eq. S14), while the compared observable is the scar-space population ⟨Πs⟩ in Fig. 3(c). Because the fit is to a different microscopic quantity than the predicted population, the Lindblad prediction is not statistically forced by the target data. There are no load-bearing self-citations: references to the authors' prior work (e.g., Refs. [20,21,49]) appear in introductory context and are not used to justify the scar construction. The main caveat is a proof gap rather than circularity: the string-cluster scattering rules (i)-(iv), especially the long-string statement that the paper itself flags as a conjecture—"we conjecture that a free long string with l≥3 can always generate a primary Krylov subsector approaching the size of the given symmetry sector up to the thermodynamic limit" (SM Sec. III)—are verified only up to L=22 and are load-bearing for the scalable exactness claim. This makes the exactness claim conditional on an unproven classification, which is a correctness risk, but it does not make the derivation equivalent to its inputs or reduce the results to the assumptions by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The ledger counts the model parameters and assumptions the construction rests on. The exact scar tower uses none; the approximate scar open-system model introduces fitted rates and pseudo-mode degrees of freedom. The key axioms are the effective constrained dynamics in the V>>J limit and the string-cluster scattering rules, which are supported by numerics only up to L=22.

free parameters (4)
  • Γn, δVn (Markovian loss rates and Lamb shifts) = extracted from numerical Gnn(t) via Eq. (S10)
    Determined by fitting the reservoir correlation function computed from the exact Hamiltonian; used in the Lindblad master equation to match scar-space decay.
  • Pseudo-mode parameters Δσ,n, λσ,n, κσ,n = K=3 modes fitted to Gnn(t) via Eq. (S14)
    Chosen to reproduce the non-Markovian correlation function; not derived from first principles.
  • Interaction strength V3 = varied (unspecified)
    Additional longer-range Ising term added ad hoc to control leakage; its value is tuned in Fig. 3(c) to demonstrate mitigation.
  • Coupling ratio ξ = ξ ≤ 1, e.g., 1, 0.8, 0.6
    Introduced in SM to modulate the coupling between scar and thermal spaces when studying approximate scar visibility; not a physical parameter of the original model.
assumptions (5)
  • domain assumption In the V >> J limit, the dynamics are governed by the constrained effective Hamiltonian Heff with conserved NII (bond number).
    Used throughout to justify the kinetic constraints; standard second-order perturbation picture for the anisotropic Heisenberg ladder.
  • domain assumption String-cluster scattering rules (i)-(iv), particularly that short strings (l ≤ 2) only partially activate large clusters (p ≥ 5) and long strings (l ≥ 3) fully activate arbitrary clusters.
    The scar construction is predicated on these rules. The rules are illustrated for small cases and tested up to L=22, but the l≥3 statement is an explicit conjecture, so the assumption extends beyond proven cases.
  • domain assumption The off-diagonal reservoir correlation function Gmn(t) is negligible for m ≠ n due to chaotic thermal-space dynamics.
    Used to reduce the generalized master equation to independent dissipative channels at each bond; checked numerically for the considered sizes, not proven.
  • domain assumption Born-Markov approximation: Gnn(t) decays much faster than the scar-space evolution timescale 1/J.
    Required to derive the Lindblad equation; the SM shows Gnn(t) is approximately delta-like, validating the approximation for the studied parameters.
  • standard math Standard quantum mechanics and exact diagonalization of small systems.
    Background for all numerical computations.
invented entities (2)
  • Auxiliary pseudo-modes aσ,n
    purpose: To model non-Markovian reservoir correlation functions in the open-system description of scar damping. These modes are mathematical devices, not physical particles.
    Introduced in SM IV with detunings, couplings, and decay rates fitted to Gnn(t); no experimental handle outside the model.
  • Environment bosonic modes b_k (eigenmodes of the projected thermal Hamiltonian)
    purpose: Represent the thermal space as a reservoir that couples to scar states through two-body loss terms.
    A reorganization of the projected Hamiltonian's eigenmodes into a bath; not an independent physical entity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Constructing Quantum Many-Body Scars from Hilbert Space Fragmentation." pith.science (2026). https://pith.science/paper/PGXYSWUO

@misc{pith2026250610806,
  author       = {Pith},
  title        = {Pith review of: Constructing Quantum Many-Body Scars from Hilbert Space Fragmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PGXYSWUO}},
  note         = {Machine review of arXiv:2506.10806}
}
read the original abstract

Quantum many-body scars (QMBS) are exotic many-body states that exhibit anomalous non-thermal behavior in an otherwise ergodic system. In this work, we demonstrate a simple, scalable and intuitive construction of QMBS in a kinetically constrained quantum model exhibiting weak Hilbert space fragmentation. We show that exact QMBS can be constructed by injecting a quasiparticle that partially activates the frozen regions in the lattice. Meanwhile, the inelastic collision between multiple quasiparticles allows for the construction of approximate scars, whose damping is governed by an emergent two-body loss. Our findings establish direct connections between quantum many-body scarring and Hilbert space fragmentation, paving the way for systematically constructing exact and approximate QMBS with nontrivial spatial connectivity. The proposed model can be readily implemented in neutral-atom quantum simulators aided by strong Rydberg interactions.

Figures

Figures reproduced from arXiv: 2506.10806 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Equilateral triangular spin ladder, where the inter-c [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Number of distinct symmetry sectors (green dots) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Connectivity graph of the symmetry sector [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weak ergodicity breaking without nonthermal eigenstates

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Nearly linear multiparticle sub-bands created by spatial modulation yield long-lived MWS revivals from spectral phase coherence among ETH-satisfying eigenstates, without nonthermal scars.

  2. Hilbert subspace imprint: a new mechanism for non-thermalization

    quant-ph 2025-06 conditional novelty 5.0 of 10

    Weak symmetry breaking or shallow-circuit state engineering can confine a quantum state to a polynomially small set of eigenstates, yielding non-thermal dynamics the authors call Hilbert subspace imprint.

Reference graph

Works this paper leans on

90 extracted references · 46 canonical work pages · cited by 2 Pith papers

  1. [1]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016)

    2016

  2. [2]

    is fragmented. First, we note that the existence of global symmetries implies that the full Hilbert space, spanned by 2 L product states |ψi⟩ in the computational basis {|•⟩, |◦⟩}, can be separated into distinct symmetry sectors Sλ,µ = span{|ψi⟩ : NI |ψi⟩ = λ |ψi⟩ ; NII |ψi⟩ = µ |ψi⟩}. In addition, within each symmetry sector, we can dynamically generate ...

  3. [3]

    As shown in Fig

    on each root state |ψi⟩. As shown in Fig. 2(a), the system has a number of Krylov subspaces ( ∼ 1.5L) which is exponentially larger than the number of symmetry sectors ( ∼L2). The lack of ob- vious conserved quantities characterizing these dynami- cally disconnected subsectors is then indicative of Hilbert space fragmentation (HSF) [ 35]. To investigate w...

  4. [4]

    can deform a single string into a different shape, while maintaining the same length [ 57]. This term can be rewritten as H [1] =Hm + Hh, where Hm =J ∑ i |◦⟩ ⟨◦|i−2 (σ+ i σ− i+1 + H.c.) |◦⟩ ⟨◦|i+3 and Hh =J ∑ i |•⟩ ⟨•|i−2 (σ+ i σ− i+1 + H.c.) |•⟩ ⟨•|i+3 induce deformations of magnon-strings and hole-strings, respec- tively. The active regions of a string i...

  5. [5]

    The eigenmode excitation b† k |0⟩ of the environment cor- responds to the k-th eigenstate (with eigenenergy ϵk) of the Hamiltonian projected onto the thermal space

    is then reformulated as Htot =HB +HS +HI , where HS = ∑ n [J(c† n+1cn + H.c.) +V3c† ncn −V3c† n+1c† ncncn+1], HB = ∑ k ϵkb† kbk, and HI = ∑ k,n (gk,nb† kcncn+1 + H.c.) describe the scar-space dynamics, the environment evolu- tion, and the system-environment coupling, respectively. The eigenmode excitation b† k |0⟩ of the environment cor- responds to the k...

  6. [6]

    Borgonovi, F

    F. Borgonovi, F. Izrailev, L. Santos, and V. Zelevinsky, Quantum chaos and thermalization in isolated systems of interacting particles, Phys. Rep. 626, 1 (2016)

    2016

  7. [7]

    Gogolin and J

    C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016)

    2016

  8. [8]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papi´ c, Quantum many- body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021)

    2021

Show all 90 references
  1. [9]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, et al. , Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017)

    2017

  2. [10]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018)

    2018

  3. [11]

    Turner, A

    C. Turner, A. Michailidis, D. Abanin, M. Serbyn, and Z. Papi´ c, Quantum scarred eigenstates in a rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018)

    2018

  4. [12]

    W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach, Phys. Rev. Lett. 122, 040603 (2019)

    2019

  5. [13]

    Iadecola, M

    T. Iadecola, M. Schecter, and S. Xu, Quantum many- body scars from magnon condensation, Phys. Rev. B 100, 184312 (2019)

    2019

  6. [14]

    Khemani, C

    V. Khemani, C. R. Laumann, and A. Chandran, Sig- natures of integrability in the dynamics of Rydberg- blockaded chains, Phys. Rev. B 99, 161101 (2019)

    2019

  7. [15]

    Lin and O

    C.-J. Lin and O. I. Motrunich, Exact Quantum Many- Body Scar States in the Rydberg-Blockaded Atom Chain, Phys. Rev. Lett. 122, 173401 (2019)

    2019

  8. [16]

    S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papi´ c, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) Dynamics and Perfect Quan- tum Many-Body Scars, Phys. Rev. Lett. 122, 220603 (2019)

    2019

  9. [17]

    Bull, J.-Y

    K. Bull, J.-Y. Desaules, and Z. Papi´ c, Quantum scars as embeddings of weakly broken Lie algebra representations, Phys. Rev. B 101, 165139 (2020)

    2020

  10. [18]

    H. Zhao, J. Vovrosh, F. Mintert, and J. Knolle, Quantum Many-Body Scars in Optical Lattices, Phys. Rev. Lett. 124, 160604 (2020)

    2020

  11. [19]

    C. J. Turner, J.-Y. Desaules, K. Bull, and Z. Papi´ c, Cor- 6 respondence Principle for Many-Body Scars in Ultracold Rydberg Atoms, Phys. Rev. X 11, 021021 (2021)

    2021

  12. [20]

    Mukherjee, S

    B. Mukherjee, S. Nandy, A. Sen, D. Sen, and K. Sen- gupta, Collapse and revival of quantum many-body scars via Floquet engineering, Phys. Rev. B 101, 245107 (2020)

    2020

  13. [21]

    van Voorden, J

    B. van Voorden, J. c. v. Min´ aˇ r, and K. Schoutens, Quan- tum many-body scars in transverse field Ising ladders and beyond, Phys. Rev. B 101, 220305 (2020)

    2020

  14. [22]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, et al. , Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021)

    2021

  15. [23]

    F. M. Surace, M. Votto, E. G. Lazo, A. Silva, M. Dal- monte, and G. Giudici, Exact many-body scars and their stability in constrained quantum chains, Phys. Rev. B 103, 104302 (2021)

    2021

  16. [24]

    J. Li, G. Giudici, and H. Pichler, Variational manifolds for ground states and scarred dynamics of blockade- constrained spin models on two- and three-dimensional lattices, Phys. Rev. Res. 6, 023146 (2024)

    2024

  17. [25]

    Giudici, F

    G. Giudici, F. M. Surace, and H. Pichler, Unravel- ing PXP Many-Body Scars through Floquet Dynamics, Phys. Rev. Lett. 133, 190404 (2024)

    2024

  18. [26]

    Lerose, T

    A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems, Phys. Rev. X 15, 011020 (2025)

    2025

  19. [27]

    D. K. Mark, C.-J. Lin, and O. I. Motrunich, Unified structure for exact towers of scar states in the Affleck- Kennedy-Lieb-Tasaki and other models, Phys. Rev. B 101, 195131 (2020)

    2020

  20. [28]

    Moudgalya, N

    S. Moudgalya, N. Regnault, and B. A. Bernevig, η- pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars, Phys. Rev. B 102, 085140 (2020)

    2020

  21. [29]

    O’Dea, F

    N. O’Dea, F. Burnell, A. Chandran, and V. Khemani, From tunnels to towers: Quantum scars from Lie algebras and q-deformed Lie algebras, Phys. Rev. Res. 2, 043305 (2020)

    2020

  22. [30]

    Pakrouski, P

    K. Pakrouski, P. N. Pallegar, F. K. Popov, and I. R. Klebanov, Many-Body Scars as a Group Invariant Sector of Hilbert Space, Phys. Rev. Lett. 125, 230602 (2020)

    2020

  23. [31]

    J. Ren, C. Liang, and C. Fang, Quasisymmetry Groups and Many-Body Scar Dynamics, Phys. Rev. Lett. 126, 120604 (2021)

    2021

  24. [32]

    Moudgalya, N

    S. Moudgalya, N. Regnault, and B. A. Bernevig, Entan- glement of exact excited states of Affleck-Kennedy-Lieb- Tasaki models: Exact results, many-body scars, and vio- lation of the strong eigenstate thermalization hypothesis, Phys. Rev. B 98, 235156 (2018)

    2018

  25. [33]

    Schecter and T

    M. Schecter and T. Iadecola, Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets, Phys. Rev. Lett. 123, 147201 (2019)

    2019

  26. [34]

    Shiraishi and T

    N. Shiraishi and T. Mori, Systematic Construction of Counterexamples to the Eigenstate Thermalization Hy- pothesis, Phys. Rev. Lett. 119, 030601 (2017)

    2017

  27. [35]

    S. Ok, K. Choo, C. Mudry, C. Castelnovo, C. Chamon, and T. Neupert, Topological many-body scar states in di- mensions one, two, and three, Phys. Rev. Res. 1, 033144 (2019)

    2019

  28. [36]

    Y. Kuno, T. Mizoguchi, and Y. Hatsugai, Flat band quantum scar, Phys. Rev. B 102, 241115 (2020)

    2020

  29. [37]

    Omiya and M

    K. Omiya and M. M¨ uller, Quantum many-body scars in bipartite Rydberg arrays originating from hidden projec- tor embedding, Phys. Rev. A 107, 023318 (2023)

    2023

  30. [38]

    Khemani, M

    V. Khemani, M. Hermele, and R. Nandkishore, Local- ization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020)

    2020

  31. [39]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: a review of exact results, Rep. Prog. Phys. 85, 086501 (2022)

    2022

  32. [40]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Annu. Rev. Condens. Matter Phys. 14, 443 (2023)

    2023

  33. [41]

    S. Pai, M. Pretko, and R. M. Nandkishore, Localization in Fractonic Random Circuits, Phys. Rev. X 9, 021003 (2019)

    2019

  34. [42]

    De Tomasi, D

    G. De Tomasi, D. Hetterich, P. Sala, and F. Pollmann, Dynamics of strongly interacting systems: From Fock- space fragmentation to many-body localization, Phys. Rev. B 100, 214313 (2019)

    2019

  35. [43]

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltoni- ans, Phys. Rev. X 10, 011047 (2020)

    2020

  36. [44]

    Pai and M

    S. Pai and M. Pretko, Fractons from confinement in one dimension, Phys. Rev. Res. 2, 013094 (2020)

    2020

  37. [45]

    Z.-C. Yang, F. Liu, A. V. Gorshkov, and T. Iadecola, Hilbert-Space Fragmentation from Strict Confinement, Phys. Rev. Lett. 124, 207602 (2020)

    2020

  38. [46]

    Hudomal, I

    A. Hudomal, I. Vasi ƒ´ a, N. Regnault, and Z. Papi´ c, Quan- tum scars of bosons with correlated hopping, Commun. Phys. 3, 99 (2020)

    2020

  39. [47]

    Moudgalya, A

    S. Moudgalya, A. Prem, R. Nandkishore, N. Regnault, and B. A. Bernevig, Thermalization and its absence within krylov subspaces of a constrained hamiltonian, in Memorial Volume for Shoucheng Zhang (World Sci- entific, 2021) Chap. 7, pp. 147–209

    2021

  40. [48]

    Zadnik and M

    L. Zadnik and M. Fagotti, The folded spin-1/2 XXZ model: I. Diagonalisation, jamming, and ground state properties, SciPost Phys. Core 4, 010 (2021)

    2021

  41. [49]

    Pozsgay, T

    B. Pozsgay, T. Gombor, A. Hutsalyuk, Y. Jiang, L. Pristy´ ak, and E. Vernier, Integrable spin chain with Hilbert space fragmentation and solvable real-time dy- namics, Phys. Rev. E 104, 044106 (2021)

    2021

  42. [50]

    C. M. Langlett and S. Xu, Hilbert space fragmentation and exact scars of generalized Fredkin spin chains, Phys. Rev. B 103, L220304 (2021)

    2021

  43. [51]

    Moudgalya and O

    S. Moudgalya and O. I. Motrunich, Hilbert Space Frag- mentation and Commutant Algebras, Phys. Rev. X 12, 011050 (2022)

    2022

  44. [52]

    Buˇ ca, Unified Theory of Local Quantum Many- Body Dynamics: Eigenoperator Thermalization Theo- rems, Phys

    B. Buˇ ca, Unified Theory of Local Quantum Many- Body Dynamics: Eigenoperator Thermalization Theo- rems, Phys. Rev. X 13, 031013 (2023)

    2023

  45. [53]

    F. Yang, H. Yarloo, H.-C. Zhang, K. Mølmer, and A. E. Nielsen, Probing Hilbert space fragmentation with strongly interacting Rydberg atoms, Phys. Rev. B 111, 144313 (2025)

    2025

  46. [54]

    Morningstar, V

    A. Morningstar, V. Khemani, and D. A. Huse, Kinetically constrained freezing transition in a dipole-conserving sys- tem, Phys. Rev. B 101, 214205 (2020)

    2020

  47. [55]

    Francica and L

    G. Francica and L. Dell’Anna, Hilbert space fragmenta- tion in a long-range system, Phys. Rev. B 108, 045127 (2023)

    2023

  48. [56]

    Wang and Z.-C

    C. Wang and Z.-C. Yang, Freezing transition in the 7 particle-conserving east model, Phys. Rev. B 108, 144308 (2023)

    2023

  49. [57]

    W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Realizing spin squeezing with Rydberg inter- actions in an optical clock, Nature 621, 734 (2023)

    2023

  50. [58]

    Steinert, P

    L.-M. Steinert, P. Osterholz, R. Eberhard, L. Festa, N. Lorenz, Z. Chen, A. Trautmann, and C. Gross, Spa- tially Tunable Spin Interactions in Neutral Atom Arrays, Phys. Rev. Lett. 130, 243001 (2023)

    2023

  51. [59]

    K. Kim, F. Yang, K. Mølmer, and J. Ahn, Realization of an Extremely Anisotropic Heisenberg Magnet in Rydberg Atom Arrays, Phys. Rev. X 14, 011025 (2024)

    2024

  52. [60]

    At both edges, two virtual sites in the state |◦⟩ are in- cluded to account for the boundary effect

  53. [61]

    See the attached movies for details, where animation 1-3 show the string deformation, string tunneling, and string- assisted hopping, respectively

  54. [62]

    See the Supplemental Material for details

  55. [64]

    Ben-Ami, M

    T. Ben-Ami, M. Heyl, and R. Moessner, Many- body cages: disorder-free glassiness from flat bands in Fock space, and many-body Rabi oscillations, arXiv:2504.13086 (2025)

    2025 arXiv

  56. [65]

    Nicolau, M

    E. Nicolau, M. Ljubotina, and M. Serbyn, Fragmenta- tion, Zero Modes, and Collective Bound States in Con- strained Models, arXiv:2504.17627 (2025)

    2025

  57. [66]

    Jonay and F

    C. Jonay and F. Pollmann, Localized Fock Space Cages in Kinetically Constrained Models, arXiv:2504.20987 (2025)

    2025 arXiv

  58. [67]

    Rosso, A

    L. Rosso, A. Biella, J. De Nardis, and L. Mazza, Dy- namical theory for one-dimensional fermions with strong two-body losses: Universal non-Hermitian Zeno physics and spin-charge separation, Phys. Rev. A 107, 013303 (2023)

    2023

  59. [68]

    J. Maki, L. Rosso, L. Mazza, and A. Biella, Loss-induced collective mode in one-dimensional Bose gases, Phys. Rev. A 110, 043315 (2024)

    2024

  60. [69]

    Garraway, Nonperturbative decay of an atomic system in a cavity, Phys

    B. Garraway, Nonperturbative decay of an atomic system in a cavity, Phys. Rev. A 55, 2290 (1997)

    1997

  61. [70]

    de Vega and D

    I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys. 89, 015001 (2017)

    2017

  62. [71]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)

    2008

  63. [72]

    W. S. Bakr, J. I. Gillen, A. Peng, S. F¨ olling, and M. Greiner, A quantum gas microscope for detecting sin- gle atoms in a Hubbard-regime optical lattice, Nature 462, 74 (2009)

    2009

  64. [73]

    Landig, L

    R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from com- peting short- and long-range interactions in an optical lattice, Nature 532, 476 (2016)

    2016

  65. [74]

    J. B. Balewski, A. T. Krupp, A. Gaj, S. Hofferberth, R. L¨ ow, and T. Pfau, Rydberg dressing: understanding of collective many-body effects and implications for ex- periments, New J. Phys. 16, 063012 (2014)

    2014

  66. [75]

    Zeiher, R

    J. Zeiher, R. van Bijnen, P. Schauß, S. Hild, J.-y. Choi, T. Pohl, I. Bloch, and C. Gross, Many-body interferome- try of a Rydberg-dressed spin lattice, Nat. Phys. 12, 1095 (2016)

    2016

  67. [76]

    Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydberg-dressed spin-flip blockade, Nat. Phys. 12, 71 (2016)

    2016

  68. [77]

    Gross and I

    C. Gross and I. Bloch, Quantum simulations with ultra- cold atoms in optical lattices, Science 357, 995 (2017)

    2017

  69. [78]

    J. A. Hines, S. V. Rajagopal, G. L. Moreau, M. D. Wahrman, N. A. Lewis, O. Markovi´ c, and M. Schleier- Smith, Spin Squeezing by Rydberg Dressing in an Ar- ray of Atomic Ensembles, Phys. Rev. Lett. 131, 063401 (2023)

    2023

  70. [79]

    Weckesser, K

    P. Weckesser, K. Srakaew, T. Blatz, D. Wei, D. Adler, S. Agrawal, A. Bohrdt, I. Bloch, and J. Zeiher, Realiza- tion of a Rydberg-dressed extended Bose Hubbard model, arXiv:2405.20128 (2024)

    2024 arXiv

  71. [80]

    A. Cao, T. L. Yelin, W. J. Eckner, N. D. Oppong, and A. M. Kaufman, Autoionization-Enhanced Rydberg Dressing by Fast Contaminant Removal, Phys. Rev. Lett. 134, 133201 (2025)

    2025

  72. [81]

    Z. Lan, M. van Horssen, S. Powell, and J. P. Garra- han, Quantum Slow Relaxation and Metastability due to Dynamical Constraints, Phys. Rev. Lett. 121, 040603 (2018)

    2018

  73. [82]

    Gopalakrishnan and B

    S. Gopalakrishnan and B. Zakirov, Facilitated quantum cellular automata as simple models with non-thermal eigenstates and dynamics, Quantum Sci. Technol. 3, 044004 (2018)

    2018

  74. [83]

    Magoni, P

    M. Magoni, P. P. Mazza, and I. Lesanovsky, Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice, Phys. Rev. Lett. 126, 103002 (2021)

    2021

  75. [84]

    Kohlert, S

    T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Exploring the Regime of Fragmentation in Strongly Tilted Fermi-Hubbard Chains, Phys. Rev. Lett. 130, 010201 (2023)

    2023

  76. [85]

    L. Zhao, P. R. Datla, W. Tian, M. M. Aliyu, and H. Loh, Observation of Quantum Thermalization Restricted to Hilbert Space Fragments and Z2k Scars, Phys. Rev. X 15, 011035 (2025)

    2025

  77. [86]

    P. R. Datla, L. Zhao, W. W. Ho, N. Klco, and H. Loh, Statistical Localization in a Rydberg Simulator of U (1) Lattice Gauge Theory, arXiv:2505.18143 (2025)

    2025

  78. [87]

    K. Lee, A. Pal, and H. J. Changlani, Frustration-induced emergent Hilbert space fragmentation, Phys. Rev. B 103, 235133 (2021)

    2021

  79. [88]

    Adler, D

    D. Adler, D. Wei, M. Will, K. Srakaew, S. Agrawal, P. Weckesser, R. Moessner, F. Pollmann, I. Bloch, and J. Zeiher, Observation of Hilbert space fragmentation and fractonic excitations in 2D, Nature 636, 80 (2024)

    2024

  80. [89]

    Y. H. Kwan, P. H. Wilhelm, S. Biswas, and S. A. Parameswaran, Minimal hubbard models of maximal hilbert space fragmentation, Phys. Rev. Lett. 134, 010411 (2025)

    2025

  81. [90]

    Buˇ ca, A

    B. Buˇ ca, A. Purkayastha, G. Guarnieri, M. T. Mitchison, D. Jaksch, and J. Goold, Quantum many-body attrac- tors, arXiv:2008.11166 (2025)

    2025 arXiv

  82. [91]

    Constructing Quantum Many-Body Scars from Hilbe rt Space Fragmentation

    P. M. Harrington, E. J. Mueller, and K. W. Murch, Engi- neered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022) . Supplemental Material for “Constructing Quantum Many-Body Scars from Hilbe rt Space Fragmentation” Fan Yang, 1, 2 Matteo Magoni, 1, 2 and...

    2022 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.