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Variational method for $\mathbb{Z}_K$ wavefunctions in spin-$J$ PXP model

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The spin-J PXP model's Z_K variational dynamics become exact and compact at J=1/2 and in the large-spin limit.

desk verdict Genuinely new analytical TDVP for Z_K spin-J PXP, with clean transfer-matrix machinery and compact J=1/2 and J→∞ limits—but the headline equations depend on a large-K approximation that is hidden, and nothing benchmarks the ansatz. read the letter →

arxiv 2501.09301 v1 pith:DIKIXTU7 submitted 2025-01-16 quant-ph cond-mat.stat-mech

Zhigang Hu , Biao Wu This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords PXPmodeltime-dependentvariationalprinciplematrixproductstatesZ_KsymmetryRydbergatomarraysquantummany-bodyscarsspin-coherentleakage
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 aims to put the variational description of Rydberg-blockaded spin chains on analytical footing for arbitrary sublattice periodicity. It constructs a bond-dimension-2 matrix-product wavefunction with $\mathbb{Z}_K$ discrete translational symmetry and derives, in closed form, the time-dependent variational principle (TDVP) equations of motion and the associated quantum-leakage error rate for the spin-$J$ PXP model. In the thermodynamic limit the expressions are rapidly convergent series, and in two opposite limits they collapse to exact, compact formulas: $J=1/2$, where the series truncate term by term, and $J\to\infty$, where the trajectory obeys classical equations of motion. If the variational manifold faithfully captures the dynamics, the work supplies a semiclassical framework for many-body revivals and quantum scars at general sublattice order.

What carries the argument

The carrying object is the $4\times 4$ transfer matrix $T_{[i,j]}$ of the $\mathbb{Z}_K$ unit cell, built from the on-site matrices $A_i(\theta_i,\phi_i)$ whose structure enforces the Rydberg blockade. Its dominant eigenvectors obey the reduction formulas $(\eta_i,0,0,1-\eta_i)T_{[i,j]}=(\eta_{j+1},0,0,1-\eta_{j+1})$ and $T_{[i,j]}(1,x_{j+1},x_{j+1},1)^T=(1,x_i,x_i,1)^T$, which let every expectation value be reduced to local contractions. This reduction, together with an exactly invertible approximation to the connected Gram matrix whose inverse decays away from the diagonal, converts the TDVP equations and the leakage rate into finite-range or rapidly convergent series.

What would settle it

Exact-diagonalize a small Rydberg-blockaded chain with L=12-18 sites, K=3 or 4, and J=1 or 3/2 for a Z_K product-state quench, and compare revival fidelity and local observables with the TDVP equations: if the exact evolution leaves the manifold faster than $\int_0^t \Gamma\,dt' \sim 1$, or if the predicted even/odd-K leakage scaling does not match the numerical error, the central claim fails.

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Extended reading notes

Core claim

The paper's central claim is that the projected dynamics of the spin-$J$ PXP model on the $\mathbb{Z}_K$-symmetric, bond-dimension-2, spin-coherent matrix-product manifold are completely characterizable by a few closed-form objects. At finite $J$, the TDVP equations (19)-(20) and the quantum leakage (D30) are rapidly convergent series whose terms are controlled by the factor $\tilde c_i = -1 + (2J\tan^2(\theta_i/2)+1)\cos^{4J}(\theta_i/2)$; because $\tilde c_i=0$ for $J=1/2$, the spin-$1/2$ dynamics and leakage reduce to the compact formulas (25)-(27). In the large-spin limit the dynamics simplify to $J\dot\theta_i = \Omega_i \sin\phi_i$ and $J\dot\phi_i = \Delta_i + \Omega_i \cos\phi_i \cot\theta_i$, and the leakage decays exponentially with $J$ for odd $K$ but only as $J^{-1/2}$ for even $K$, a parity asymmetry the authors flag as an open question about the ansatz.

Load-bearing premise

The load-bearing assumption is that the bond-dimension-2, $\mathbb{Z}_K$-symmetric spin-coherent matrix-product ansatz is an adequate variational manifold for the PXP dynamics of interest; every derived equation describes the projection onto this manifold, and its quality is only measured by the internally computed leakage $\Gamma^2$.

Editorial extensions

If this is right

  • For J=1/2, the Z_K variational dynamics become coupled local first-order equations, so revivals for period-K states can be studied with the same analytical ease as the original two-period case.
  • In the large-spin limit, the variational trajectory is governed by classical pendulum-like equations, giving an explicit semiclassical picture whose validity time is set by the computed leakage.
  • The leakage rate is independent of the detuning profile, so inhomogeneous detunings do not alter the variational error estimate along the projected trajectory.
  • Because the inverse Gram matrix elements decay with distance, the infinite sums in the equations of motion can be truncated at finite range with controlled error in the thermodynamic limit.
  • The derived leakage predicts that the quantum-classical correspondence time scales exponentially with J for odd K but only as the square root of J for even K, making the classical limit sharply sensitive to sublattice periodicity.

Reading between the lines

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

  • A natural benchmark would be exact diagonalization of small Rydberg-blockaded chains with K=3 or 4; if the revival fidelity tracks the TDVP trajectory and the error grows no faster than the integrated leakage, the ansatz is quantitatively reliable rather than merely illustrative.
  • The exponential-versus-sqrt(J) timescale asymmetry is sharp enough to test directly: spin-J chains with odd and even K should show very different sensitivity to the classical limit, which would settle whether the asymmetry is physical or an artifact of bond dimension 2.
  • The same reduction formulas may extend to other constrained Hamiltonians with Z_K density-wave order, such as blockade models with longer-range interactions, giving a general calculus for higher-period TDVP.
  • For K=2 the formulas should reproduce the known period-doubling revival picture, so checking that the series truncation recovers that trajectory is a quick consistency test of the new conventions.
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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 / 5 minor

Summary. The paper develops a time-dependent variational principle (TDVP) treatment of the one-dimensional spin- J PXP model with detuning, using a bond-dimension-2 matrix-product-state ansatz with Z_K discrete translational symmetry. The authors derive closed-form expressions for the variational energy, the TDVP equations of motion, and the quantum leakage rate in the thermodynamic limit, presenting them as rapidly convergent series in terms of products of coefficients c~_i. They specialize to J=1/2, where the series truncate exactly, and to the classical limit J→∞, where the dynamics reduce to coupled first-order equations for θ_i and φ_i and the leakage scales with J in a K-parity-dependent way. The paper contains extensive appendices in which the transfer-matrix algebra, Gram-matrix inversion, and leakage computation are carried out analytically; no numerical benchmark against exact dynamics is reported.

Significance. If correct, this would be the first closed-form Z_K generalization of the Z_2 MPS-TDVP program of Ho, Choi, Pichler, and Lukin, and it could provide a useful analytical tool for Rydberg-atom arrays with sublattice symmetry. The algebraic core is original and nontrivial: the transfer-matrix reduction formulas, the explicit Gram-matrix inverse, and the closed-form leakage expressions are substantial achievements, and the spot-checks I have made of selected reductions (e.g., the K=1 η formula and the J=1/2 truncation) are internally consistent. The paper is also honest about the main physical limitation, namely that the variational manifold is not tested against the true PXP dynamics. The significance is conditional on two points that the manuscript does not resolve: whether the closed-form results extend to small values of K, and whether the Z_K-symmetric MPS ansatz is an adequate variational manifold for the scarred dynamics of interest.

major comments (4)
  1. [Sec. IV and App. C, Eqs. (C20)-(C21)] The main-text TDVP equations (19)-(20), and their specializations (25)-(26) and (30), are derived under the assumption stated in Sec. IV that "K is sufficient large such that the eigenvalue λ2=β[1,K] is negligible" — that is, β[1,K]=0. The exact inverse Gram matrix in Eq. (C21) contains, however, a factor (1−β[1,K])^{-1} inside the definition of c~_i (Eq. (C20)) and a global denominator 1−∏_{m=1}^{K} c~_m in every off-diagonal entry. These factors are dropped in the main text. For fixed physical period K, e.g., K=2 or 3, β[1,K] is generally O(1) and 1−∏c~ is not close to 1; in the large-J limit near the north pole c~_i→−1, so for even K the denominator can become exponentially small. The sentence following Eq. (10) — "We can enforce the periodicity of xi in the large unit cell to recover the small K case" — is not a derivation and does not show that the omitted denominators cancel or become negligible. Consequently, the closed-form equations are rigorously established only in the large-K limit (or, formally, when β[1,K]=0), not for general Z_K as claimed. In particular, for J=1/2 the identity c~_i=0 follows from Eq. (C23) only after β[1,K] has been set to zero; with the exact expression in Eq. (C20) the simplification does not occur.
  2. [Sec. VI, Eq. (30)] The large-J leakage formula (30) and the associated odd/even-K timescale asymmetry inherit the same β[1,K]=0 and 1−∏c~=1 approximations. This is not a minor technicality: the parity-dependent behavior of Γ^2 is exactly controlled by whether ∏c~ is close to 1, which is the very factor that is omitted. Near the north pole, c~_i≈−1, so for even K the exact denominator 1−∏c~ can be exponentially small in J, while for odd K it is close to 2. The authors' own caveat in Sec. VI — "we are unsure whether this feature is just a reflection on the limitation of our simple ansatz" — attaches to the very prediction (Eq. (30)) that depends on this approximation. The manuscript should either retain the exact denominators in the large-J analysis or provide a controlled estimate showing that 1−∏c~=1+o(1) along the trajectories of interest; without this, the parity-dependent timescale claim is unsubstantiated.
  3. [Sec. VI, text after Eq. (20)] The convergence claim "Since |c~_i|<1 it is often reasonable to truncate the summation until ∏m c~m becomes negligible" does not establish rapid convergence. For generic θ_i away from θ=0, |c~_i|→1 as J→∞, and products of an even number of such factors tend to 1, not to 0. Thus the series in Eqs. (19)-(20) are not necessarily rapidly convergent in the large-J regime; the formal J→∞ limit is obtained by the vanishing of the cos^{4J−2}(θ/2) prefactors, not by decay of the products. A quantitative statement about ∏c~_m along the relevant trajectories is needed to support the paper's central claim that the variational dynamics and error rate can be expressed as rapidly convergent series.
  4. [Secs. IV-VI (general)] The paper never tests the variational ansatz (Eq. (5)) against exact diagonalization, tensor-network simulation, or the established Z_2 results of Ref. [7]. The internal leakage Γ^2 is an estimate of the error within the chosen manifold, but it is not a validation that the manifold captures the relevant directions of the true PXP dynamics for the initial states of interest. For example, the J=1/2 equations (25)-(26) are claimed to reproduce the Z_2 TDVP program, but no explicit comparison with Ref. [7] is shown. Adding a small-system exact-diagonalization benchmark or a comparison with existing numerical data for the PXP revival dynamics would substantially strengthen the physical relevance of the closed-form results.
minor comments (5)
  1. [Eq. (20) and surrounding text] The definition of c~_i after Eq. (20) uses θ_j on the right-hand side but θ_i on the left; this is a typographical inconsistency that should be fixed.
  2. [Appendix C, Eq. (C20)] The quantity z_i in the expression c~_i = z_i − a_i b_i / c_i is not defined in the text before it is used; the reader must infer it from the preceding matrix A, and an explicit definition would improve clarity.
  3. [Appendices D, Eq. (D30)] In Eq. (D30) the summation symbol "k∑_{i=1}" uses a lowercase k in one place; it should be K for consistency with the rest of the equation.
  4. [Throughout, especially Eqs. (10), (16), (19)-(20)] The notation "cos4J θi/2" is ambiguous; it should be written as cos^{4J}(θ_i/2) to avoid confusion between an exponent and a factor, and similarly for other powers of cos and sin.
  5. [References] References [8] and [21] are the same article (Turner et al., Nature Physics 14, 745 (2018)) and should be merged or cross-referenced rather than listed twice.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the TDVP derivation is self-contained, with no fitted parameters, no self-citation chain, and no input-output equivalence.

full rationale

The paper's central claims are derived algebraically from the fixed variational ansatz and the physical Hamiltonian H = sum_i (Omega_i P s^x_i P + Delta_i s^z_i). The variational parameters (theta_i, phi_i) are dynamical unknowns, not fitted constants; the only inputs are the physical parameters Omega_i and Delta_i. The transfer matrix T[i,j] is solved by explicit induction in Appendix B, the dominant eigenvectors and reduction formulae are proven from the transfer-matrix eigenvalues, and the inverse Gram matrix is obtained analytically in Appendix C2. The J=1/2 simplification is an exact algebraic identity (c~_i = -1 + (1 + 2J tan^2(theta_i/2)) cos^{4J}(theta_i/2) = 0 for J=1/2), and the J->infinity equations are obtained by taking a genuine large-J limit, not by fitting or renaming. The paper's own caveat that the odd/even-K timescale difference at large J may reflect 'the limitation of our simple ansatz' (Sec. VI) is a correctness and approximation concern, not circularity: nothing in the derivation is defined in terms of the result it purports to predict. The large-K assumption beta[1,K] -> 0 used in simplifying c~_i is an uncontrolled asymptotic step for fixed small K, but it is an approximation whose accuracy is not demonstrated, not a circular reduction of the output to the input. No fitted parameters are renamed as predictions, no load-bearing claims are justified solely by self-citations, and no known empirical result is relabeled as a derivation.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

All numbered inputs are model parameters Omega and Delta; the coefficients x_i, eta_i, and c~_i are derived functions of the variational variables. No free parameters are fitted to data, and no new physical entities (particles, forces, or conserved quantities) are postulated beyond the variational MPS construction itself. The load-bearing structure is the variational projection principle plus the adequacy of the Z_K MPS manifold; the latter is the main unvalidated premise.

assumptions (5)
  • domain assumption The TDVP projection of quantum dynamics onto a chosen variational manifold is a valid approximation, and the quantum leakage Lambda^2 (Eq. 2) measures its instantaneous error, with the criterion integral of Lambda dt <~ 1 for trustworthiness.
    Sec. II, Eqs. (1)-(2), following Dirac (Ref. 11) and the TDVP literature (Refs. 12-14, 20). Every result in the paper describes this projected dynamics rather than the exact Schrodinger evolution.
  • domain assumption The Z_K-symmetric, bond-dimension-2 MPS ansatz (Eqs. 4-5) is an adequate variational manifold for the PXP physics of interest.
    Sec. IV. Adequacy is assessed only through the internally computed leakage Gamma^2; no external benchmark (exact diagonalization, tensor networks, or experiment) is provided.
  • standard math The transfer matrix has a single dominant eigenvalue lambda=1 with |lambda_2| = |beta[1,K]| < 1, so Perron-Frobenius controls the thermodynamic-limit contractions; the all-theta=pi configuration is excluded.
    Sec. IV after Eq. (7): |beta| = product of (1 - x^2), which reaches 1 only when every theta_i = pi.
  • standard math Standard spin-coherent-state identities (Gilmore generating functions, Vaidman formulas, Tables I-II) are used for all on-site expectation values.
    Appendix A, Eqs. (A1)-(A8), citing Ref. [32]. These are background results, used but not re-derived, and the entire derivation inherits their validity.
  • domain assumption The J to infinity limit is taken after the thermodynamic limit and away from the poles theta=0 and theta=pi, where cos^{2J}(theta/2) does not decay.
    Sec. VI before Eq. (28). The classical-limit equations and the even/odd-K timescale statements are only claimed in this regime.
invented entities (1)
  • Z_K-symmetric bond-dimension-2 MPS ansatz for spin-J PXP dynamics
    purpose: Variational trial wavefunction family that encodes the Rydberg blockade and enables closed-form TDVP dynamics and leakage computation for general sublattice period K
    A variational construction introduced for analytic tractability. Its physical validity is checked only via the in-paper leakage Gamma^2; the paper provides no comparison with exact numerics or experiment, so there is no independent falsifiable handle here.

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Pith. "Pith review of Variational method for $\mathbb{Z}_K$ wavefunctions in spin-$J$ PXP model." pith.science (2026). https://pith.science/paper/DIKIXTU7

@misc{pith2026250109301,
  author       = {Pith},
  title        = {Pith review of: Variational method for $\mathbbZ_K$ wavefunctions in spin-$J$ PXP model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIKIXTU7}},
  note         = {Machine review of arXiv:2501.09301}
}
abstract

We investigate the approach of time-dependent variational principle (TDVP) for the one-dimensional spin-$J$ PXP model with detuning, which is relevant for programmable Rydberg atom arrays. The variational manifold is chosen as the minimally entangled $\mathbb{Z}_K$ matrix-product-states (MPS). We demonstrate that variational dynamics and variational error can be expressed as rapidly convergent series in the thermodynamic limit. In particular, for $J=1/2$ and the limiting case $J\rightarrow \infty$, the TDVP results become exact and significantly simplified.

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Forward citations

Cited by 1 Pith paper

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Works this paper leans on

39 extracted references · 33 canonical work pages · cited by 1 Pith paper

  1. [7]

    (D13) One can see that (VarZZ )ij = ∆ i∆ j J 2 Gc φ i,φ j. (D14) The ZX term is VarZX = −L K K∑ i=1 i+K∑ j=i+1 ηiηi+1∆ iΩ j(1 − cosθi) ( sinθj cosφ j + 2(−1 +xj+1)x2 j tanθj 2 cosφ j ) β[i+1,j −1] 1 −β[1,K ] − L K K∑ i=1 i−1∑ j=i−K ηjηj+1∆ iΩ j(1 − cosθi) ( sinθj cosφ j + 2(−1 +xj+1)x2 j tanθj 2 cosφ j ) β[j+1,i −1] 1 −β[1,K ] + L K K∑ i=1 ∆ iΩ i ηi 2J ( ...

    work page

  2. [1]

    Using the notation from Eq

    Gram matrix We first calculate the connected Gram matrix Gc µ i,ν i+k ≡ ⟨∂µ iΨ |∂νi+kΨ ⟩c. Using the notation from Eq. ( B22), ( B23), and ( B12), and applying Perron-Frobenius theorem, we obtain the following expression for 1 ≤k ≤K − 1 Gc µ i,ν i+k = L K ∑ m≥0 (li| ¯∂µTi ·T[i+1,i +k+mK−1] ·∂νTi+k+mK|ri+k+mK+1)c + L K ∑ m≤−1 (li+k+mK|∂νTi+k+mK ·T[i+k+mK+1,...

    work page

  3. [2]

    Unlike in ⟨∂µ iψ |H|ψ ⟩c, the projector P can not be simply omitted in the energy variance

    once we solve the energy variance ⟨Ψ |H 2|Ψ ⟩c. Unlike in ⟨∂µ iψ |H|ψ ⟩c, the projector P can not be simply omitted in the energy variance. It is useful to decompose P into product of two-site operators Pi,i +1, which satisfy local relation Pi,i +1Ai ·Ai+1 =Ai ·Ai+1 and A∗ i ·A∗ i+1Pi,i +1 =A∗ i ·A∗ i+1, and commute with sz j . This allows us to reduce te...

    work page

  4. [3]

    Mathematically, that is Pi,i +1(∂µ iAi)Ai+1 = (∂µ iAi)Ai+1, P i,i +1Ai(∂µ i+1Ai+1) = Ai(∂µ i+1Ai+1)

    ⟨Ψ |H|∂µ Ψ ⟩c We begin by noting that the matrix elements of ( ∂µ iAi)Ai+1 and Ai(∂µ i+1Ai+1) do not contain any (Ii −Pi)|θi,φ i⟩ ⊗ (Ii+1 −Pi+1)|θi+1,φ i+1⟩ components. Mathematically, that is Pi,i +1(∂µ iAi)Ai+1 = (∂µ iAi)Ai+1, P i,i +1Ai(∂µ i+1Ai+1) = Ai(∂µ i+1Ai+1). (C27) The equation implies that the operation of the partial derivative com mutes with ...

    work page

  5. [4]

    Inverting a K ×K matrix is generally a challenging task

    Inverse of the Gram matrix To solve the equations of motion, we need to calculate the inverse of the Gram matrix (ImGc θ,φ )−1. Inverting a K ×K matrix is generally a challenging task. However, we notice that ImGc θ,φ is closely related to the matrix A Aij =            aibi ∏ i+K−1 m=i+1zm ifi =j, aibj ∏ j−1 m=i+1zm ifi<j, aibj ∏ j+K−1 m=i+1zm ...

    work page

  6. [5]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran , H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Probing m any-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017)

    work page 2017

  7. [6]

    This residual term is given by Rφ j ≡ L K ( −ηj tanφ j 2 Ω j cosφ j(sinθj + 2x2 j (−1 +xj+1) tanθj 2 ) )

    TDVP equations To account for the contributions from the term Im Gc θ , φ in Re ⟨∂µ j Ψ |H|Ψ ⟩c, we define a residual term Rφ j for Re ⟨∂φ j Ψ |H|Ψ ⟩c, which excludes contributions involving (Im Gc θ , φ )jl. This residual term is given by Rφ j ≡ L K ( −ηj tanφ j 2 Ω j cosφ j(sinθj + 2x2 j (−1 +xj+1) tanθj 2 ) ) . (C38) Using this definition, along with the...

    work page

  8. [8]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang , D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev , A. Vishwanath, M. Greiner, 35 V. Vuleti´ c, and M. D. Lukin, Probing topological spin liqui ds on a programmable quantum simulator, Science 374, 1242 (2021)

    work page 2021

Show all 39 references
  1. [9]

    Pichler, S.-T

    H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Quantum optimization for maximum independent set using ryd berg atom arrays (2018), arXiv:1808.10816 [quant-ph]

    2018 arXiv

  2. [10]

    Ljubotina, B

    M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, Optima l steering of matrix product states and quantum many-body scars, PRX Quantum 3, 030343 (2022)

    2022

  3. [11]

    Sachdev, K

    S. Sachdev, K. Sengupta, and S. M. Girvin, Mott insulator s in strong electric fields, Phys. Rev. B 66, 075128 (2002)

    2002

  4. [12]

    Haegeman, J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Ve rschelde, and F. Verstraete, Time- dependent variational principle for quantum lattices, Phys. Rev. Lett. 107, 070601 (2011)

    2011

  5. [13]

    Samajdar, W

    R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, and S. Sachd ev, Complex density wave orders and quantum phase transitions in a model of square-la ttice rydberg atom arrays, Phys. Rev. Lett. 124, 103601 (2020)

    2020

  6. [14]

    W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic orb its, entanglement, and quantum many-body scars in constrained models: Matrix p roduct state approach, Phys. Rev. Lett. 122, 040603 (2019)

    2019

  7. [15]

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

    2018

  8. [16]

    Serbyn, D

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

    2021

  9. [17]

    Khemani, C

    V. Khemani, C. R. Laumann, and A. Chandran, Signatures o f integrability in the dynamics of rydberg-blockaded chains, Phys. Rev. B 99, 161101 (2019)

    2019

  10. [18]

    P. A. M. Dirac, Note on exchange phenomena in the thomas a tom, Mathematical Proceedings of the Cambridge Philosophical S ociety 26, 376–385 (1930)

    1930

  11. [19]

    V. S. Liu, M. Bintz, M. Block, R. Samajdar, J. Kemp, and N. Y. Yao, Supersolidity and simplex phases in spin-1 rydberg atom arr ays (2024), arXiv:2407.17554 [cond-mat.quant-gas]

    2024 arXiv

  12. [20]

    Hackl, T

    L. Hackl, T. Guaita, T. Shi, J. Haegeman, E. Demler, and J . I. Cirac, Geometry of variational methods: dynamics of closed quantum systems, SciPost Phys. 9, 048 (2020)

    2020

  13. [21]

    Vanderstraeten, J

    L. Vanderstraeten, J. Haegeman, and F. Verstraete, Tan gent-space methods for uniform matrix 36 product states, SciPost Phys. Lect. Notes , 7 (2019)

    2019

  14. [22]

    A. A. Michailidis, C. J. Turner, Z. Papi´ c, D. A. Abanin, and M. Serbyn, Slow quantum ther- malization and many-body revivals from mixed phase space, Phys. Rev. X 10, 011055 (2020)

    2020

  15. [23]

    spin down

    is (li−1|TPi−1 ·Tsx i ·TPi+1sx i+1|ri+2)c, (24) where the subscript ‘c’ denotes the removal of the disconnectedpart (li|Tsx i |ri+1)·(li+1|Tsx i+1|ri+2). For further details, the full calculation of the quantum leakage is in A ppendix D. In previous discussion, we outlined the...

  16. [24]

    E. J. Heller, Time dependent variational approach to se miclassical dynamics, The Journal of Chemical Physics 64, 63 (1976)

    1976

  17. [25]

    Affleck, T

    I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59, 799 (1987)

    1987

  18. [26]

    Zhang, A

    Y. Zhang, A. Gaddie, H.-V. Do, G. W. Biedermann, and R. J. Lewis-Swan, Simulating a two-component bose-hubbard model with imbalanced hopping in a rydberg tweezer array, Phys. Rev. A 109, 053317 (2024)

    2024

  19. [27]

    Evrard, A

    B. Evrard, A. Pizzi, S. I. Mistakidis, and C. B. Dag, Quan tum many-body scars from unstable periodic orbits, Phys. Rev. B 110, 144302 (2024)

    2024

  20. [28]

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

    2018

  21. [29]

    G.-X. Su, H. Sun, A. Hudomal, J.-Y. Desaules, Z.-Y. Zhou , B. Yang, J. C. Halimeh, Z.- S. Yuan, Z. Papi´ c, and J.-W. Pan, Observation of many-body s carring in a bose-hubbard quantum simulator, Phys. Rev. Res. 5, 023010 (2023)

    2023

  22. [30]

    E. H. Lieb, The classical limit of quantum spin systems, Commun. Math. Phys. 31, 327 (1973)

    1973

  23. [31]

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

    2024

  24. [32]

    Kerschbaumer, M

    A. Kerschbaumer, M. Ljubotina, M. Serbyn, and J.-Y. Des aules, Quantum many-body scars beyond the pxp model in rydberg simu lators (2024), arXiv:2410.18913 [quant-ph]

    2024 arXiv

  25. [33]

    Zhang, D

    S.-Y. Zhang, D. Yuan, T. Iadecola, S. Xu, and D.-L. Deng, Extracting quantum many-body scarred eigenstates with matrix product states, Phys. Rev. Lett. 131, 020402 (2023)

    2023

  26. [34]

    Reini´ c, D

    N. Reini´ c, D. Jaschke, D. Wanisch, P. Silvi, and S. Montangero, Finite-temperature rydberg ar- rays: Quantum phases and entanglement characterization, Phys. Rev. Res. 6, 033322 (2024) . 37

    2024

  27. [35]

    C. J. Turner, J.-Y. Desaules, K. Bull, and Z. Papi´ c, Cor respondence principle for many-body scars in ultracold rydberg atoms, Phys. Rev. X 11, 021021 (2021)

    2021

  28. [36]

    Hallam, J

    A. Hallam, J. G. Morley, and A. G. Green, The lyapunov spe ctra of quantum thermalisation, Nature Communications 10, 2708 (2019)

    2019

  29. [37]

    Omran, H

    A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wan g, S. Ebadi, H. Bernien, A. S. Zi- brov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Generati on and manipulation of schr¨ odi...

    2019

  30. [38]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeg hini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Controlling quantum many-body dynamics in d riven rydberg atom arrays, Science 371, 1355 (2021)

    2021

  31. [39]

    Zhang, D

    W.-M. Zhang, D. H. Feng, and R. Gilmore, Coherent states : Theory and some applications, Rev. Mod. Phys. 62, 867 (1990) . 38

    1990

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Reviewed August 10, 2026 · model on record in the stance chip above.