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arxiv: 2605.19606 · v1 · pith:3Y433Q7Cnew · submitted 2026-05-19 · ❄️ cond-mat.stat-mech · math-ph· math.MP· quant-ph

Proof of the absence of local conserved quantities in the Holstein model

Fuga Ishii , Mizuki Yamaguchi This is my paper

Pith reviewed 2026-05-20 02:29 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech math-phmath.MPquant-ph
keywords Holstein modellocal conserved quantitiesnonintegrabilityelectron-phonon couplingthermalizationHolstein-Hubbard modelone-dimensional chains
5
0 comments X

The pith

The one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator.

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

The paper proves that the one-dimensional Holstein model, describing electrons interacting with local lattice vibrations, lacks any additional local operators that are conserved besides the total energy and the number of electrons. A sympathetic reader would care because assumptions about the absence of such quantities underpin explanations of thermalization, where systems evolve to equilibrium states, and transport phenomena in quantum materials. The result extends this nonintegrability to the Holstein-Hubbard model that also includes direct electron repulsion. This advances understanding by confirming the property in systems where fermions and bosons are coupled locally.

Core claim

The central claim is that any operator supported on a finite contiguous segment of the chain that commutes with the Holstein Hamiltonian must be a linear combination of the Hamiltonian and the total fermion number. The authors establish this by direct computation of the commutation conditions on the local terms involving electron creation, annihilation, and phonon displacements. The same absence of nontrivial local conserved quantities is shown when an on-site Hubbard interaction term is added.

What carries the argument

The definition of a local conserved quantity as an operator whose support is confined to a finite number of consecutive lattice sites, combined with the requirement that its commutator with the Hamiltonian vanishes identically.

If this is right

  • The model can be treated as nonintegrable for purposes of discussing thermalization dynamics.
  • Transport coefficients are expected to follow the behavior typical of chaotic quantum systems without extra symmetries.
  • The result applies equally to the Holstein-Hubbard model, broadening the class of electron-phonon systems where integrability is ruled out.
  • Proof techniques for nonintegrability now cover mixed statistical systems of electrons and phonons.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar locality-based arguments could be tested in two-dimensional versions or with long-range couplings to see if the absence persists.
  • Numerical studies of time evolution in the Holstein model should exhibit ergodic behavior consistent with this nonintegrability.
  • Extensions might connect to understanding how local coupling prevents the emergence of additional constants of motion in polaronic systems.

Load-bearing premise

The conserved quantities are required to be strictly local operators acting only within finite contiguous segments of the one-dimensional lattice.

What would settle it

Finding or constructing an operator supported on a small number of sites that commutes with the Holstein Hamiltonian but cannot be expressed as a combination of the Hamiltonian and total particle number would disprove the claim.

Figures

Figures reproduced from arXiv: 2605.19606 by Fuga Ishii, Mizuki Yamaguchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Level-spacing statistics of the Holstein model (1). Panels (a) and (b) show the nonintegrable case [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
read the original abstract

Absence of local conserved quantities, or \textit{nonintegrability}, is often assumed when discussing various phenomena in quantum many-body systems, such as thermalization and transport. However, no concrete proof of this property is known in electron--phonon coupled systems, a typical setting for condensed matter physics. In this paper, we show that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. We further show that the absence of nontrivial local conserved quantities also holds for the more general Holstein--Hubbard model. Our result has accomplished an advance in nonintegrability proofs by expanding their scope to systems in which particles with different statistical properties are mixed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to prove that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. It further claims that the same absence holds for the Holstein-Hubbard model. The proof expands prior nonintegrability techniques to mixed fermionic-bosonic systems, with locality defined via operators of finite contiguous support on the chain.

Significance. If the central proof holds, the result is significant: it supplies the first rigorous demonstration of nonintegrability in electron-phonon systems, a setting where such absence had been assumed but never proven. This strengthens the basis for thermalization and transport studies in condensed-matter models and extends nonintegrability methods to systems with mixed particle statistics. The explicit mathematical construction is a clear strength.

major comments (2)
  1. [§3] §3, the core commutator argument: the claim that any local Q satisfying [H, Q] = 0 must be a linear combination of H and N_f rests on cancellation of all non-local terms. The handling of boundary contributions from the finite-support definition of Q in the infinite-volume limit is not accompanied by explicit estimates or vanishing arguments, which is load-bearing for the locality constraint.
  2. [§5] §5 (Holstein-Hubbard extension): the additional Hubbard interaction is inserted into the commutator, yet the derivation does not separately verify that the U term cannot generate new local conserved quantities for finite U; this step is required to justify the claim that the result carries over unchanged.
minor comments (1)
  1. [§2] The notation for the phonon operators and the precise support condition on Q could be stated as an explicit equation early in §2 to avoid ambiguity when reading the commutator expansions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and for the detailed comments, which help clarify the presentation of the proof. We address each major comment below.

read point-by-point responses

  1. Referee: §3, the core commutator argument: the claim that any local Q satisfying [H, Q] = 0 must be a linear combination of H and N_f rests on cancellation of all non-local terms. The handling of boundary contributions from the finite-support definition of Q in the infinite-volume limit is not accompanied by explicit estimates or vanishing arguments, which is load-bearing for the locality constraint.

    Authors: We agree that the boundary contributions merit a more explicit treatment to make the argument fully rigorous. In the definition used in §3, locality means that Q has strictly finite contiguous support on the infinite chain. The commutator [H, Q] then receives contributions only from Hamiltonian terms whose support overlaps the boundary of Q's support; all other terms commute to zero. Because [H, Q] = 0 must hold as an operator identity, these finitely many boundary operators must themselves cancel. In the revised manuscript we will insert a short lemma (or expanded paragraph) that isolates these boundary terms, shows they are supported on a fixed number of sites independent of the position of Q, and demonstrates that the specific form of the Holstein electron-phonon coupling forces their coefficients to vanish separately from the bulk cancellation. This supplies the explicit vanishing argument requested. revision: yes

  2. Referee: §5 (Holstein-Hubbard extension): the additional Hubbard interaction is inserted into the commutator, yet the derivation does not separately verify that the U term cannot generate new local conserved quantities for finite U; this step is required to justify the claim that the result carries over unchanged.

    Authors: The extension to the Holstein-Hubbard model is obtained simply by adding the on-site Hubbard term U ∑_i n_{i↑} n_{i↓} to the Hamiltonian and repeating the same commutator analysis. Because this term is strictly local (on-site) and commutes with the total fermion number N_f, it does not enlarge the space of local operators that could commute with the full Hamiltonian. Any candidate local Q that commutes with the extended H must still satisfy the identical cancellation conditions arising from the hopping, phonon, and electron-phonon terms; the additional [U, Q] contribution remains local and is absorbed into the same boundary-bulk decomposition already used for the Holstein model. We will add a brief clarifying paragraph in §5 that makes this reasoning explicit and notes that the electron-phonon coupling continues to enforce the same linear dependence on H and N_f for any finite U. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the mathematical proof

full rationale

The paper presents a direct mathematical proof of the absence of nontrivial local conserved quantities in the 1D Holstein model (and Holstein-Hubbard extension) by showing that only the Hamiltonian and total fermion number satisfy the required commutation relations under the standard finite-support locality definition on contiguous lattice segments. No steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the argument expands prior nonintegrability techniques to mixed fermionic-bosonic systems in a self-contained manner without renaming known results or smuggling ansatzes. This is the expected outcome for a pure existence/absence proof in this domain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proof rests on standard definitions of local operators and commutation relations in quantum lattice systems; no free parameters or new entities are introduced.

axioms (2)
  • domain assumption Local conserved quantities are operators supported on finite contiguous segments that commute with the Hamiltonian.
    This definition is invoked to classify what counts as a nontrivial local conserved quantity.
  • domain assumption The Holstein Hamiltonian has the standard local form with electron hopping, on-site energy, and local electron-phonon coupling.
    The specific Hamiltonian is the starting point for the commutation analysis.

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Reference graph

Works this paper leans on

102 extracted references · 102 canonical work pages · 2 internal anchors

  1. [1]

    Inputs of type i In this section, we treatk-support inputsA k of type i. The conclusion of step 1 analysis for this type is sum- marized in the following Lemma: Lemma 1(step 1 analysis for type i).Assume ˆQk is a k-local conserved quantity of the one-dimensional Hol- stein model(1)witht̸= 0,g̸= 0, andω̸= 0. The coefficients ofA k i of type i satisfy the f...

    work page

  2. [2]

    Inputs of type ii Next, we treatk-support inputsA k i of type ii. The conclusion of step 1 analysis for this type is summarized in the following Lemma: Lemma 2(Step 1 analysis for type ii).Assume ˆQk is ak-local conserved quantity of the one-dimensional Holstein model(1)witht̸= 0,g̸= 0, andω̸= 0. qAk i = 0holds for anyA k i of type ii. Proof.Owing to the ...

    work page

  3. [3]

    None of this type of input generatesB k+1

    Inputs of type iii Finally, we examinek-support inputsA k i of type iii. None of this type of input generatesB k+1. Then, we cannot obtain any valid relation for type iii inputsA k i at this point. B. Proof step 2: Basic relations for products with widthk. We next derive further constraints from the condi- tions onk-support outputs, i.e.,r Bk i = 0 for al...

    work page

  4. [4]

    Inputs of type i Again, we treatA k of type i. The conclusion of step 2 analysis for this type is summarized in the following Lemma: Lemma 3(Step 2 analysis for type i).Assume ˆQk is a k-local conserved quantity of the one-dimensional Hol- stein model(1)witht̸= 0,g̸= 0, andω̸= 0. The coefficients ofA k i of type i satisfy the following relation for anyi: ...

    work page

  5. [5]

    These constraints are useful in step 3 when analyzing inputs forB k−1

    Constraints onA k−1 In addition, we derive constraints on co- efficients of (k−1)-support inputs written asA k−1 i =C 1(x1, y1)iC2(x2, y2)i+k−2 with (C1, C2)∈ {(ˆc,ˆc †),(ˆc†,ˆc)}. These constraints are useful in step 3 when analyzing inputs forB k−1. The conclusion of this analysis is summarized in the following Lemma: Lemma 4.Assume ˆQk is ak-local cons...

    work page

  6. [6]

    Inputs of type iii Next, we treatA k i of type iii. The conclusion of step 2 analysis for this type is summarized in the following Lemma: Lemma 5(Step 2 analysis for type iii).Assume ˆQk is ak-local conserved quantity of the one-dimensional Holstein model(1)witht̸= 0,g̸= 0, andω̸= 0. qAk i = 0holds for anyA k i of type iii. Proof.First, forA k i = I(x 1, ...

    work page

  7. [7]

    Step 3 fork= 3 We first consider the casek= 3. Lemma 6(Step 3 analysis for the casek= 3).As- sume ˆQk=3 is a3-local conserved quantity of the one- dimensional Holstein model(1)witht̸= 0,g̸= 0, and ω̸= 0.q Ak=3 i = 0holds for anyA k=3 i of type i. 10 Proof.By Lemma 3, 3-support inputA k=3 of type i has zero coefficients in most cases. Below, we will prove ...

    work page

  8. [8]

    Lemma 7(Step 3 analysis for the case 4≤k≤L/2)

    Step 3 for4≤k≤L/2 Next, consider the case 4≤k≤L/2. Lemma 7(Step 3 analysis for the case 4≤k≤L/2). Assume ˆQk is ak-local conserved quantity of the one- dimensional Holstein model(1)witht̸= 0,g̸= 0, and ω̸= 0.q Ak i = 0holds for anyA k i of type i. Proof.By Lemma 3,k-support inputA k of type i has zero coefficients in most cases. Below, we will prove that ...

    work page

  9. [9]

    First, we considerA 2 i =e 1 i e2 i+1 of type i and type ii

    Proof fork= 2case We show that the only 2-local conserved quantity is the Hamiltonian ˆHitself up to the freedom of adding 1-local conserved quantities. First, we considerA 2 i =e 1 i e2 i+1 of type i and type ii. Without loss of generality, we assumee 2 ̸=I(x, y). We first discuss explicitly the case in which the right end is e2 = ˆc(x2, y2). Namely, tak...

    work page

  10. [10]

    We discussA 1 i = ˆn(x, y)i explicitly

    Proof fork= 1case First, we consider the candidatesA 1 = ˆc(x, y),ˆc†(x, y),ˆn(x, y). We discussA 1 i = ˆn(x, y)i explicitly. The commutator with the right hopping term gives [ˆn(x, y)i,ˆc† i ˆci+1] = ˆc†(x, y)iˆci+1.(130) If (x, y)̸= (0,0), this output is generated only by this input, and thereforeq ˆn(x,y)i = 0. When (x, y) = (0,0), however, the same ou...

    work page

  11. [11]

    In this case, it can be diagonalized by the Lang– Firsov transformation [61]

    The caset= 0 Whent= 0, the Hamiltonian contains only onsite terms. In this case, it can be diagonalized by the Lang– Firsov transformation [61]. Introducing the operator ˆS= g ω X i ˆni(ˆb† i − ˆbi),(A1) and defining the transformed Hamiltonian by ˆH ′ =e − ˆS ˆHe ˆS,(A2) one obtains ˆH ′ =− g2 ω X i ˆn2 i +ω X i ˆb† iˆbi =− g2 ω X i ˆc† i ˆci +ω X i ˆb† ...

    work page

  12. [12]

    This model is therefore directly diagonalizable

    The caseg= 0 Wheng= 0, the Hamiltonian reduces to ˆH=t X i (ˆc† i ˆci+1 + ˆc† i+1ˆci) +ω X i ˆb† iˆbi,(A4) namely, a sum of a free-fermion tight-binding Hamil- tonian and localized phonons. This model is therefore directly diagonalizable. As for local conserved quantities, the boson number operator at each site ˆb† iˆbi is obviously conserved. In addition...

    work page

  13. [13]

    Indeed, at each site the operator ˆb† i + ˆbi, which corresponds to the phonon displacement, com- mutes with the Hamiltonian

    The caseω= 0 Whenω= 0, it is also easy to see that the system has an extensive number of independent local conserved quantities. Indeed, at each site the operator ˆb† i + ˆbi, which corresponds to the phonon displacement, com- mutes with the Hamiltonian. In this sense, the system is integrable when counted by the number of indepen- dent local conserved quantities

    work page

  14. [14]

    Numerical analysis of level statistics To illustrate the parameter dependence of integrabil- ity, we numerically investigate the level spacing statis- tics [1, 83] of the Holstein model by exact diagonal- ization. For the ordinary one-dimensional Holstein model with periodic boundary conditions, both the total fermion number ˆN= P i ˆni and the crystal mo...

    work page

  15. [15]

    As a spinful extension of the spinless basis in Eqs

    Proof of Lemma 8 Proof.The proof follows a strategy similar to that of Theorem 1. As a spinful extension of the spinless basis in Eqs. (8) and (9), we use the followingl-support basis starting from sitei: Al i,B l i =e iei+1 . . . ei+l−1,(C1) ej ∈ n fj,↑fj,↓(ˆb† j)xˆby j |f j,σ ∈ {I,ˆcj,σ,ˆc† j,σ,ˆnj,σ}, σ∈ {↑,↓}, x, y∈Z ≥0 o ,(C2) withe i, ei+l−1 ̸=I( ˆb...

    work page

  16. [16]

    Proof of Lemma 9 Proof.We prove the statement separately fork= 2 and k= 1. a. Proof fork= 2case We show that the only 2-local conserved quantity is the Hamiltonian ˆHitself up to multiplication by a con- stant and the freedom of adding 1-local conserved quan- tities. ConsiderA 2 i =e 1 i e2 i+1 of type i and type ii. Without loss of generality, we assumee...

    work page

  17. [17]

    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)

    work page 2016

  18. [18]

    T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Ther- malization and prethermalization in isolated quantum systems: a theoretical overview, J. Phys. B51, 112001 (2018)

    work page 2018

  19. [19]

    J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A43, 2046 (1991)

    work page 2046

  20. [20]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E50, 888 (1994)

    work page 1994

  21. [21]

    Rigol, V

    M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum sys- tems, Nature452, 854 (2008)

    work page 2008

  22. [22]

    Rigol, V

    M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Re- laxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons, Phys. Rev. Lett.98, 050405 (2007)

    work page 2007

  23. [23]

    Vidmar and M

    L. Vidmar and M. Rigol, Generalized gibbs ensemble in integrable lattice models, J. Stat. Mech.: Theory Exp. 2016(6), 064007

    work page 2016

  24. [24]

    M. S. Green, Markoff random processes and the sta- tistical mechanics of time-dependent phenomena. ii. ir- reversible processes in fluids, J. Chem. Phys.22, 398 (1954)

    work page 1954

  25. [25]

    Kubo, Statistical-mechanical theory of irreversible processes

    R. Kubo, Statistical-mechanical theory of irreversible processes. i. general theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957)

    work page 1957

  26. [26]

    Mazur, Non-ergodicity of phase functions in certain systems, Physica43, 533 (1969)

    P. Mazur, Non-ergodicity of phase functions in certain systems, Physica43, 533 (1969)

    work page 1969

  27. [27]

    Suzuki, Ergodicity, constants of motion, and bounds for susceptibilities, Physica51, 277 (1971)

    M. Suzuki, Ergodicity, constants of motion, and bounds for susceptibilities, Physica51, 277 (1971)

    work page 1971

  28. [28]

    Zotos, F

    X. Zotos, F. Naef, and P. Prelovsek, Transport and con- servation laws, Phys. Rev. B55, 11029 (1997)

    work page 1997

  29. [29]

    Saito, Strong evidence of normal heat conduction in a one-dimensional quantum system, Europhys

    K. Saito, Strong evidence of normal heat conduction in a one-dimensional quantum system, Europhys. Lett.61, 34 (2003)

    work page 2003

  30. [30]

    Sirker, Transport in one-dimensional integrable quan- tum systems, SciPost Phys

    J. Sirker, Transport in one-dimensional integrable quan- tum systems, SciPost Phys. Lect. Notes , 17 (2020)

    work page 2020

  31. [31]

    Kinoshita, T

    T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum newton’s cradle, Nature440, 900 (2006)

    work page 2006

  32. [32]

    O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Emergent hydrodynamics in integrable quantum sys- tems out of equilibrium, Phys. Rev. X6, 041065 (2016)

    work page 2016

  33. [33]

    Bertini, M

    B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Transport in out-of-equilibriumxxzchains: Exact pro- files of charges and currents, Phys. Rev. Lett.117, 207201 (2016)

    work page 2016

  34. [34]

    De Nardis, B

    J. De Nardis, B. Doyon, M. Medenjak, and M. Panfil, Correlation functions and transport coefficients in gen- eralised hydrodynamics, J. Stat. Mech.: Theory Exp. 2022(1), 014002

    work page 2022

  35. [35]

    Doyon, S

    B. Doyon, S. Gopalakrishnan, F. Møller, J. Schmied- mayer, and R. Vasseur, Generalized hydrodynamics: A perspective, Phys. Rev. X15, 010501 (2025)

    work page 2025

  36. [36]

    Shiraishi, Proof of the absence of local conserved quantities in the xyz chain with a magnetic field, Euro- phys

    N. Shiraishi, Proof of the absence of local conserved quantities in the xyz chain with a magnetic field, Euro- phys. Lett.128, 17002 (2019)

    work page 2019

  37. [37]

    Hokkyo, Rigorous Test for Quantum Integrability and Nonintegrabili ty, (preprint, 2025)

    A. Hokkyo, Rigorous test for quantum integrability and nonintegrability (2025), arXiv:2501.18400 [cond- mat.stat-mech]

    work page arXiv 2025

  38. [38]

    Chiba, Proof of absence of local conserved quantities in the mixed-field ising chain, Phys

    Y. Chiba, Proof of absence of local conserved quantities in the mixed-field ising chain, Phys. Rev. B109, 035123 (2024)

    work page 2024

  39. [39]

    Chiba and Y

    Y. Chiba and Y. Yoneta, Exact thermal eigenstates of nonintegrable spin chains at infinite temperature, Phys. Rev. Lett.133, 170404 (2024)

    work page 2024

  40. [40]

    H. K. Park and S. Lee, Graph-theoretical proof of non- integrability in quantum many-body systems: Appli- cation to the pxp model, Phys. Rev. B111, L081101 (2025)

    work page 2025

  41. [41]

    H. K. Park and S. Lee, Nonintegrability in the pxp model: A graph-theoretical approach, Phys. Rev. B 111, 085104 (2025)

    work page 2025

  42. [42]

    Shiraishi, Absence of local conserved quantity in the heisenberg model with next-nearest-neighbor interac- tion: N

    N. Shiraishi, Absence of local conserved quantity in the heisenberg model with next-nearest-neighbor interac- tion: N. shiraishi, J. Stat. Phys.191, 114 (2024)

    work page 2024

  43. [43]

    Yamaguchi, Y

    M. Yamaguchi, Y. Chiba, and N. Shiraishi, Proof of the absence of local conserved quantities in general spin- 1/2 chains with symmetric nearest-neighbor interaction (2024), arXiv:2411.02163 [cond-mat.stat-mech]

    work page arXiv 2024

  44. [44]

    Yamaguchi, Y

    M. Yamaguchi, Y. Chiba, and N. Shiraishi, Complete classification of integrability and non-integrability for spin-1/2 chain with symmetric nearest-neighbor inter- action (2024), arXiv:2411.02162 [cond-mat.stat-mech]

    work page arXiv 2024

  45. [45]

    Hokkyo, M

    A. Hokkyo, M. Yamaguchi, and Y. Chiba, Absence of nontrivial local conserved quantities in the spin- 1 bilinear-biquadratic chain and its anisotropic exten- sions, Phys. Rev. Res.7, 043297 (2025)

    work page 2025

  46. [46]

    H. K. Park and S. Lee, Proof of nonintegrability of the spin-1 bilinear-biquadratic chain model, Phys. Rev. B 111, 134444 (2025)

    work page 2025

  47. [47]

    Chiba, Proof of absence of local conserved quantities 22 in two- and higher-dimensional quantum ising models, Phys

    Y. Chiba, Proof of absence of local conserved quantities 22 in two- and higher-dimensional quantum ising models, Phys. Rev. B111, 195130 (2025)

    work page 2025

  48. [48]

    Shiraishi and H

    N. Shiraishi and H. Tasaki, TheS= 1/2XYandXYZ models on the two-or higher-dimensional hypercubic lat- tice do not possess nontrivial local conserved quantities, Ann. Henri Poincar´ e (2026)

    work page 2026

  49. [49]

    Shiraishi, Complete classification of integrability and non-integrability ofS= 1/2 spin chains with symmetric next-nearest-neighbor interaction, J

    N. Shiraishi, Complete classification of integrability and non-integrability ofS= 1/2 spin chains with symmetric next-nearest-neighbor interaction, J. Stat. Phys.192, 170 (2025)

    work page 2025

  50. [50]

    Futami and H

    M. Futami and H. Tasaki, Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice, J. Math. Phys.66(2025)

    work page 2025

  51. [51]

    Shiraishi and M

    N. Shiraishi and M. Yamaguchi, Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains (2025), arXiv:2504.14315 [cond- mat.stat-mech]

    work page arXiv 2025

  52. [52]

    W.-M. Fan, K. Hao, Y.-Y. Chen, K. Zhang, X.-H. Wang, and V. Korepin, Absence of local conserved charges of the fredkin spin chain and its truncated versions, Phys. Rev. B112, 205124 (2025)

    work page 2025

  53. [53]

    Futami, Absence of nontrivial local conserved quan- tities in the hubbard model on the two or higher di- mensional hypercubic lattice (2025), arXiv:2507.20106 [cond-mat.stat-mech]

    M. Futami, Absence of nontrivial local conserved quan- tities in the hubbard model on the two or higher di- mensional hypercubic lattice (2025), arXiv:2507.20106 [cond-mat.stat-mech]

    work page arXiv 2025

  54. [54]

    Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains

    M. Yamaguchi and N. Shiraishi, Violating the all- or-nothing picture of local charges in non-hermitian bosonic chains (2026), arXiv:2603.10972 [cond-mat.stat- mech]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  55. [55]

    Nozawa and K

    Y. Nozawa and K. Fukai, Explicit construction of local conserved quantities in theXYZspin-1/2 chain, Phys. Rev. Lett.125, 090602 (2020)

    work page 2020

  56. [56]

    Yamada and K

    K. Yamada and K. Fukai, Matrix product operator rep- resentations for the local conserved quantities of the Heisenberg chain, SciPost Phys. Core6, 069 (2023)

    work page 2023

  57. [57]

    Fukai and K

    K. Fukai and K. Yamada, Matrix product operator rep- resentations for the local conserved quantities of the spin-1/2XYZchain (2026), arXiv:2601.09245 [nlin.SI]

    work page arXiv 2026

  58. [58]

    Fukai, All local conserved quantities of the one- dimensional hubbard model, Phys

    K. Fukai, All local conserved quantities of the one- dimensional hubbard model, Phys. Rev. Lett.131, 256704 (2023)

    work page 2023

  59. [59]

    Fukai, Proof of completeness of the local conserved quantities in the one-dimensional hubbard model, J

    K. Fukai, Proof of completeness of the local conserved quantities in the one-dimensional hubbard model, J. Stat. Phys.191, 70 (2024)

    work page 2024

  60. [60]

    Holstein, Studies of polaron motion: Part i

    T. Holstein, Studies of polaron motion: Part i. the molecular-crystal model, Ann. Phys.8, 325 (1959)

    work page 1959

  61. [61]

    Caux and J

    J.-S. Caux and J. Mossel, Remarks on the notion of quantum integrability, J. Stat. Mech.: Theory Exp. 2011(02), P02023

    work page 2011

  62. [62]

    Giannetti, M

    C. Giannetti, M. Capone, D. Fausti, M. Fabrizio, F. Parmigiani, and D. Mihailovic, Ultrafast optical spectroscopy of strongly correlated materials and high- temperature superconductors: a non-equilibrium ap- proach, Adv. Phys.65, 58 (2016)

    work page 2016

  63. [63]

    Sayyad and M

    S. Sayyad and M. Eckstein, Coexistence of excited po- larons and metastable delocalized states in photoin- duced metals, Phys. Rev. B91, 104301 (2015)

    work page 2015

  64. [64]

    Murakami, P

    Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, In- teraction quench in the holstein model: Thermaliza- tion crossover from electron- to phonon-dominated re- laxation, Phys. Rev. B91, 045128 (2015)

    work page 2015

  65. [65]

    Mitri´ c, V

    P. Mitri´ c, V. Jankovi´ c, N. Vukmirovi´ c, and D. Tanaskovi´ c, Spectral functions of the holstein polaron: Exact and approximate solutions, Phys. Rev. Lett.129, 096401 (2022)

    work page 2022

  66. [66]

    Fehske, G

    H. Fehske, G. Wellein, and A. R. Bishop, Spatiotempo- ral evolution of polaronic states in finite quantum sys- tems, Phys. Rev. B83, 075104 (2011)

    work page 2011

  67. [67]

    Dorfner, L

    F. Dorfner, L. Vidmar, C. Brockt, E. Jeckelmann, and F. Heidrich-Meisner, Real-time decay of a highly excited charge carrier in the one-dimensional holstein model, Phys. Rev. B91, 104302 (2015)

    work page 2015

  68. [68]

    Brockt, F

    C. Brockt, F. Dorfner, L. Vidmar, F. Heidrich-Meisner, and E. Jeckelmann, Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium, Phys. Rev. B92, 241106 (2015)

    work page 2015

  69. [69]

    Stolpp, J

    J. Stolpp, J. Herbrych, F. Dorfner, E. Dagotto, and F. Heidrich-Meisner, Charge-density-wave melting in the one-dimensional holstein model, Phys. Rev. B101, 035134 (2020)

    work page 2020

  70. [70]

    Nomura, Machine learning quantum states — ex- tensions to fermion–boson coupled systems and excited- state calculations, J

    Y. Nomura, Machine learning quantum states — ex- tensions to fermion–boson coupled systems and excited- state calculations, J. Phys. Soc. Jpn.89, 054706 (2020)

    work page 2020

  71. [71]

    A. Ning, L. Yang, and G.-W. Chern, Recurrent con- volutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems, Phys. Rev. E 113, 015307 (2026)

    work page 2026

  72. [72]

    ten Brink, S

    M. ten Brink, S. Gr¨ aber, M. Hopjan, D. Jansen, J. Stolpp, F. Heidrich-Meisner, and P. E. Bl¨ ochl, Real- time non-adiabatic dynamics in the one-dimensional holstein model: Trajectory-based vs exact methods, J. Chem. Phys.156(2022)

    work page 2022

  73. [73]

    Mitri´ c, Dynamical quantum typicality: Simple method for investigating transport properties applied to the holstein model, Phys

    P. Mitri´ c, Dynamical quantum typicality: Simple method for investigating transport properties applied to the holstein model, Phys. Rev. B111, 195140 (2025)

    work page 2025

  74. [74]

    Goleˇ z, J

    D. Goleˇ z, J. Bonˇ ca, L. Vidmar, and S. A. Trugman, Relaxation dynamics of the holstein polaron, Phys. Rev. Lett.109, 236402 (2012)

    work page 2012

  75. [75]

    Kogoj, L

    J. Kogoj, L. Vidmar, M. Mierzejewski, S. A. Trug- man, and J. Bonˇ ca, Thermalization after photoexcita- tion from the perspective of optical spectroscopy, Phys. Rev. B94, 014304 (2016)

    work page 2016

  76. [76]

    Jansen, J

    D. Jansen, J. Stolpp, L. Vidmar, and F. Heidrich- Meisner, Eigenstate thermalization and quantum chaos in the holstein polaron model, Phys. Rev. B99, 155130 (2019)

    work page 2019

  77. [77]

    Lang and Y

    I. Lang and Y. A. Firsov, Kinetic theory of semicon- ductors with low mobility, Sov. Phys. JETP16, 1301 (1963)

    work page 1963

  78. [78]

    Zhang, E

    C. Zhang, E. Jeckelmann, and S. R. White, Dynamical properties of the one-dimensional holstein model, Phys. Rev. B60, 14092 (1999)

    work page 1999

  79. [79]

    Jansen and F

    D. Jansen and F. Heidrich-Meisner, Thermal and optical conductivity in the holstein model at half filling and finite temperature in the luttinger-liquid and charge- density-wave regime, Phys. Rev. B108, L081114 (2023)

    work page 2023

  80. [80]

    Jankovi´ c, Holstein polaron transport from numeri- cally “exact” real-time quantum dynamics simulations, J

    V. Jankovi´ c, Holstein polaron transport from numeri- cally “exact” real-time quantum dynamics simulations, J. Chem. Phys.159(2023)

    work page 2023

Showing first 80 references.