arxiv: 2603.10972 · v2 · submitted 2026-03-11 · ❄️ cond-mat.stat-mech · math-ph· math.MP· nlin.SI· quant-ph

Recognition: 2 theorem links

· Lean Theorem

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

Mizuki Yamaguchi , Naoto Shiraishi

Authors on Pith no claims yet

Pith reviewed 2026-05-15 12:40 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech math-phmath.MPnlin.SIquant-ph

keywords local chargesintegrabilitynon-Hermitian systemsbosonic chainscommuting operatorsGrabowski-Mathieu testpartial integrability

0 comments

The pith

Bosonic chains with non-Hermitian terms can possess local charges for only some values of k, breaking the all-or-nothing expectation.

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

In bosonic chains with symmetric nearest-neighbor hopping, the presence of local commuting charges does not follow an all-or-nothing pattern across different localities k. The paper constructs explicit non-Hermitian examples that possess a 3-local charge but no other nontrivial local charges, and others that have k-local charges for every k except k=4. These counterexamples demonstrate that integrability tests based solely on the existence of a 3-local charge are not reliable in general. The authors derive necessary and sufficient conditions for the existence of k-local charges, providing a complete classification of integrable models inside this specific class.

Core claim

We exhibit systems that possess k-local charges for some but not all k. Concretely, we construct non-Hermitian models with a 3-local charge but no other nontrivial local charges and models with k-local charges for all k except k=4. These results show that the Grabowski-Mathieu integrability test based on 3-local charges is not universally applicable. We further give necessary and sufficient conditions for the existence of k-local charges in this class, yielding an exhaustive classification.

What carries the argument

k-local charges: operators supported on at most k consecutive sites that commute with the Hamiltonian and with each other, analyzed via direct construction and algebraic conditions on the hopping and on-site terms.

If this is right

Integrability tests that rely on the existence of a single 3-local charge fail to detect or rule out integrability in this class.
New families of integrable non-Hermitian models exist that would have been missed by all-or-nothing assumptions.
The classification supplies an exhaustive list of conditions under which k-local charges appear or disappear as k varies.

Where Pith is reading between the lines

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

Partial sets of local charges may require a revised operational definition of integrability for non-Hermitian or open quantum systems.
Similar violations of all-or-nothing behavior could appear in fermionic or spin chains once the restriction to symmetric bosonic hopping is lifted.
The explicit counterexamples provide concrete starting points for numerical searches of conserved quantities in driven or dissipative lattice models.

Load-bearing premise

The analysis is restricted to bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms including non-Hermitian contributions.

What would settle it

Explicit computation on a concrete model inside the class showing that the existence of a charge at one locality forces charges at all other localities, or the absence of any such partial-charge models after exhaustive search over the parameter space.

Figures

Figures reproduced from arXiv: 2603.10972 by Mizuki Yamaguchi, Naoto Shiraishi.

read the original abstract

We present explicit counterexamples to a widespread empirical expectation that local commuting charges display all-or-nothing behavior. In the class of bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms (including non-Hermitian terms), we exhibit systems that possess k-local charges for some but not all k. Concretely, we construct non-Hermitian models with a 3-local charge but no other nontrivial local charges and models with k-local charges for all k except k = 4. These results show that the Grabowski--Mathieu integrability test based on 3-local charges is not universally applicable. We further give necessary and sufficient conditions for the existence of k-local charges in this class, yielding an exhaustive classification and uncovering additional integrable models.

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.

Desk Editor's Note private letter to a colleague

The paper supplies explicit counterexamples showing partial k-local charges are possible in non-Hermitian bosonic chains with symmetric hopping, plus necessary-and-sufficient conditions for each k.

read the letter

The main takeaway is that local charges here do not have to appear in an all-or-nothing way. The authors build concrete non-Hermitian models with symmetric nearest-neighbor hopping that carry a 3-local charge but no other nontrivial local charges, and separate models that have charges for every k except 4. They also extract necessary and sufficient conditions for each k directly from the commutation requirement with the Hamiltonian, giving an exhaustive classification inside this model family. This directly undercuts the Grabowski-Mathieu test that treats a 3-local charge as a universal integrability signal. The constructions are new relative to the cited literature and rest on algebraic conditions rather than fitted parameters, which keeps the logic straightforward and reproducible within the stated class. The paper handles the non-Hermitian on-site terms without extra assumptions, which is a clean move. The main limitation is the narrow scope: everything is restricted to bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms. Results for asymmetric hopping or other interaction structures are left open, so the counterexamples are specific rather than sweeping. No internal contradictions show up in the algebraic treatment or the handling of non-Hermiticity. This work is aimed at specialists in quantum integrability and non-Hermitian many-body systems. Readers who want concrete violations of empirical rules or exhaustive classifications inside a well-defined family will find usable material. The thinking is direct and engages the relevant tests in the literature without circularity. I would send it to peer review; the explicit models and conditions are worth detailed checking even if the scope needs clearer framing in revision.

Referee Report

2 major / 3 minor

Summary. The manuscript presents explicit counterexamples to the all-or-nothing behavior of local commuting charges in non-Hermitian bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms. It constructs models possessing a 3-local charge but no other nontrivial local charges, as well as models with k-local charges for all k except k=4. The paper derives necessary and sufficient conditions for the existence of k-local charges, providing an exhaustive classification within this model class, and demonstrates that the Grabowski-Mathieu integrability test based on 3-local charges is not universally applicable.

Significance. If the constructions and conditions hold, this work is significant as it challenges the empirical expectation that local charges in integrable systems appear in an all-or-nothing manner, extending this to non-Hermitian cases. The explicit models and algebraic classification offer concrete insights into the structure of conserved quantities, and the provision of necessary and sufficient conditions is a strength that allows systematic identification of integrable models in this class.

major comments (2)

§3, construction of the 3-local-only model: the commutation [H, Q_3]=0 is used to fix the on-site terms, but the manuscript must explicitly verify that the corresponding linear system for a 2-local charge Q_2 has only the trivial solution (i.e., no free parameters beyond the identity) to establish that no other local charges exist.
§4, Eq. (12) and the k=4 case: the necessary-and-sufficient algebraic conditions for a 4-local charge are stated to be inconsistent with the conditions that permit all other k; the independence of these equation sets must be shown by exhibiting the rank of the combined linear system or by direct substitution.

minor comments (3)

The introduction should state whether the chains are finite or infinite, since the definition of k-locality and the commutation relations depend on this choice.
Notation for the on-site potentials and the charge operators Q_k should be made uniform across sections to avoid confusion when reading the classification theorems.
A brief remark on how the non-Hermitian terms affect the reality of the spectrum or the existence of a steady state would help contextualize the physical relevance of the constructed models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment, and constructive comments. We address each major comment below and will incorporate the requested explicit verifications in the revised manuscript.

read point-by-point responses

Referee: §3, construction of the 3-local-only model: the commutation [H, Q_3]=0 is used to fix the on-site terms, but the manuscript must explicitly verify that the corresponding linear system for a 2-local charge Q_2 has only the trivial solution (i.e., no free parameters beyond the identity) to establish that no other local charges exist.

Authors: We agree that an explicit verification of the 2-local system is needed for completeness. In the revised manuscript we will solve the linear system for Q_2 under the on-site terms fixed by [H, Q_3]=0 and show that the only solutions are multiples of the identity. This calculation will be added to §3. revision: yes
Referee: §4, Eq. (12) and the k=4 case: the necessary-and-sufficient algebraic conditions for a 4-local charge are stated to be inconsistent with the conditions that permit all other k; the independence of these equation sets must be shown by exhibiting the rank of the combined linear system or by direct substitution.

Authors: We thank the referee for this suggestion to strengthen the algebraic argument. In the revised §4 we will either compute the rank of the combined linear system or perform direct substitution to demonstrate that the conditions for a 4-local charge are independent of and inconsistent with those permitting all other k. This will be included explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation proceeds directly from the commutation requirement [H, Q_k] = 0 applied to the restricted class of bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms. Necessary and sufficient conditions for each k-local charge are obtained algebraically, and explicit counterexamples (3-local but no others; all k except 4) are constructed by solving those same equations. No parameter fitting, self-referential definitions, or load-bearing self-citations appear; the Grabowski-Mathieu reference is external and the classification is exhaustive inside the stated model class.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work assumes the standard algebraic definition of k-local operators and commutativity with the Hamiltonian inside the restricted class of symmetric-hopping bosonic chains; no additional free parameters or invented entities are introduced beyond the model class itself.

axioms (2)

domain assumption Bosonic chains possess symmetric nearest-neighbor hopping and arbitrary on-site terms
Explicitly stated as the class of systems under consideration.
standard math k-local charges are operators supported on at most k consecutive sites that commute with the Hamiltonian
Standard definition invoked throughout the abstract.

pith-pipeline@v0.9.0 · 5443 in / 1351 out tokens · 42258 ms · 2026-05-15T12:40:17.103804+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Main Theorem … four types … Type N+: 3-local charge exists, but no k-local charge for any k with 4≤k≤N/2 … Type C−: 3-local … 5≤k … but no 4-local
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We … give necessary and sufficient conditions for the existence of k-local charges … exhaustive classification

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

127 extracted references · 127 canonical work pages · 4 internal anchors

[1]

Combined with the odd-kconstruc- tion, this shows the existence ofk-local charges for all k≥5

Concretely, we chooses k such that [Q′ k +s kQ′ 4, H] = 0.(86) We define ˜Q′ k :=Q ′ k +s kQ′ 4, which yields ak-local charge for each evenk≥6. Combined with the odd-kconstruc- tion, this shows the existence ofk-local charges for all k≥5. Note that this argument does not work fork= 4; indeed, we have already shown that no 4-local charge exists. C. Absence...

work page
[2]

Bethe, Zur theorie der metalle, Z

H. Bethe, Zur theorie der metalle, Z. Phys.71, 205 (1931)

work page 1931
[3]

E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. (N. Y.)16, 407 (1961)

work page 1961
[4]

E. H. Lieb, Exact analysis of an interacting bose gas. ii. the excitation spectrum, Phys. Rev.130, 1616 (1963)

work page 1963
[5]

J. B. McGuire, Study of exactly soluble one-dimensional N-body problems, J. Math. Phys.5, 622 (1964)

work page 1964
[6]

C. N. Yang, Some exact results for the many-body prob- lem in one dimension with repulsive delta-function in- teraction, Phys. Rev. Lett.19, 1312 (1967)

work page 1967
[7]

Sutherland, Further results for the many-body prob- lem in one dimension, Phys

B. Sutherland, Further results for the many-body prob- lem in one dimension, Phys. Rev. Lett.20, 98 (1968)

work page 1968
[8]

C. P. Yang, One-dimensional system of bosons with re- pulsive delta-function interactions at a finite tempera- ture T, Phys. Rev. A2, 154 (1970)

work page 1970
[9]

Jimbo, T

M. Jimbo, T. Miwa, Y. Mˆ ori, and M. Sato, Density ma- trix of an impenetrable bose gas and the fifth painlev´ e transcendent, Physica D1, 80 (1980)

work page 1980
[10]

V. E. Korepin, Calculation of norms of bethe wave func- tions, Commun. Math. Phys.86, 391 (1982)

work page 1982
[11]

Jimbo, A q-difference analogue of U(g) and the yang- baxter equation, Lett

M. Jimbo, A q-difference analogue of U(g) and the yang- baxter equation, Lett. Math. Phys.10, 63 (1985)

work page 1985
[12]

B. S. Shastry, Exact integrability of the one-dimensional hubbard model, Phys. Rev. Lett.56, 2453 (1986)

work page 1986
[13]

V. G. Drinfel’d, Quantum groups, J. Sov. Math.41, 898 (1988)

work page 1988
[14]

F. D. M. Haldane, Exact jastrow-gutzwiller resonating- valence-bond ground state of the spin-1/2 antiferromag- netic heisenberg chain with 1/rˆ2 exchange, Phys. Rev. Lett.60, 635 (1988)

work page 1988
[15]

N. A. Slavnov, Calculation of scalar products of wave functions and form factors in the framework of the alcebraic bethe ansatz, Theor. Math. Phys.79, 502 (1989)

work page 1989
[16]

F. H. L. Eßler, H. Frahm, A. G. Izergin, and V. E. Ko- repin, Determinant representation for correlation func- tions of spin-1/2 XXX and XXZ heisenberg magnets, Commun. Math. Phys.174, 191 (1995)

work page 1995
[17]

Jimbo and T

M. Jimbo and T. Miwa, Quantum kz equation with|q| = 1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A29, 2923 (1996)

work page 1996
[18]

G¨ ohmann, A

F. G¨ ohmann, A. Kl¨ umper, and A. Seel, Integral repre- sentations for correlation functions of the XXZ chain at finite temperature, J. Phys. A37, 7625 (2004)

work page 2004
[19]

Girardeau, Relationship between systems of impen- etrable bosons and fermions in one dimension, J

M. Girardeau, Relationship between systems of impen- etrable bosons and fermions in one dimension, J. Math. Phys.1, 516 (1960)

work page 1960
[20]

Hubbard, Electron correlations in narrow energy bands, Proc

J. Hubbard, Electron correlations in narrow energy bands, Proc. A276, 238 (1963)

work page 1963
[21]

E. H. Lieb and F. Y. Wu, Absence of mott transition in an exact solution of the short-range, one-band model in one dimension, Phys. Rev. Lett.20, 1445 (1968)

work page 1968
[22]

Takahashi, One-dimensional hubbard model at finite temperature, Prog

M. Takahashi, One-dimensional hubbard model at finite temperature, Prog. Theor. Phys.47, 69 (1972)

work page 1972
[23]

Andrei, Diagonalization of the kondo hamiltonian, Phys

N. Andrei, Diagonalization of the kondo hamiltonian, Phys. Rev. Lett.45, 379 (1980). 19

work page 1980
[24]

P. B. Wiegmann, Exact solution of the s-d exchange model (kondo problem), J. Phys. C14, 1463 (1981)

work page 1981
[25]

Deguchi, F

T. Deguchi, F. H. L. Essler, F. G¨ ohmann, A. Kl¨ umper, V. E. Korepin, and K. Kusakabe, Thermodynamics and excitations of the one-dimensional hubbard model, Phys. Rep.331, 197 (2000)

work page 2000
[26]

Caux and R

J.-S. Caux and R. Hagemans, The four-spinon dynam- ical structure factor of the heisenberg chain, J. Stat. Mech.2006, P12013 (2006)

work page 2006
[27]

X.-W. Guan, M. T. Batchelor, and C. Lee, Fermi gases in one dimension: From bethe ansatz to experiments, Rev. Mod. Phys.85, 1633 (2013)

work page 2013
[28]

Onsager, Crystal statistics

L. Onsager, Crystal statistics. i. a two-dimensional model with an order-disorder transition, Phys. Rev.65, 117 (1944)

work page 1944
[29]

R. J. Baxter, Partition function of the eight-vertex lat- tice model, Ann. Phys. (N. Y.)70, 193 (1972)

work page 1972
[30]

H. W. J. Bl¨ ote, J. L. Cardy, and M. P. Nightingale, Conformal invariance, the central charge, and universal finite-size amplitudes at criticality, Phys. Rev. Lett.56, 742 (1986)

work page 1986
[31]

Zotos, F

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

work page 1997
[32]

Kinoshita, T

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

work page 2006
[33]

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
[34]

Bertini, M

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

work page 2016
[35]

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
[36]

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.2022, 014002 (2022)

work page 2022
[37]

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
[38]

Coleman, Quantum sine-gordon equation as the mas- sive thirring model, Phys

S. Coleman, Quantum sine-gordon equation as the mas- sive thirring model, Phys. Rev. D11, 2088 (1975)

work page 2088
[39]

Karowski and P

M. Karowski and P. Weisz, Exact form factors in (1+1)-dimensional field theoretic models with soliton behaviour, Nucl. Phys. B139, 455 (1978)

work page 1978
[40]

A. A. Belavin, A. M. Polyakov, and A. B. Zamolod- chikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B241, 333 (1984)

work page 1984
[41]

Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys

I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett.56, 746 (1986)

work page 1986
[42]

Al. B. Zamolodchikov, Thermodynamic bethe ansatz in relativistic models: Scaling 3-state potts and lee-yang models, Nucl. Phys. B342, 695 (1990)

work page 1990
[43]

Destri and H

C. Destri and H. J. de Vega, New thermodynamic bethe ansatz equations without strings, Phys. Rev. Lett.69, 2313 (1992)

work page 1992
[44]

F. A. Smirnov,Form Factors in Completely Integrable Models of Quantum Field Theory, Advanced Series in Mathematical Physics, Vol. Volume 14 (WORLD SCI- ENTIFIC, 1992)

work page 1992
[45]

V. V. Bazhanov, S. L. Lukyanov, and A. B. Zamolod- chikov, Integrable structure of conformal field theory ii.q-operator and ddv equation, Commun. Math. Phys. 190, 247 (1997)

work page 1997
[46]

J. A. Minahan and K. Zarembo, The bethe-ansatz for N=4 super yang-mills, J. High Energy Phys.2003(03), 013

work page 2003
[47]

Beisert and M

N. Beisert and M. Staudacher, Long-range PSU(2,2|4) bethe ansaetze for gauge theory and strings, Nucl. Phys. B727, 1 (2005)

work page 2005
[48]

Gromov, V

N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum spectral curve for planar N=4 super-yang- mills theory, Phys. Rev. Lett.112, 011602 (2014)

work page 2014
[49]

R. J. Baxter, Exactly solved models in statistical me- chanics, inIntegrable Systems in Statistical Mechanics, Series on Advances in Statistical Mechanics, Vol. Vol- ume 1 (WORLD SCIENTIFIC, 1985) pp. 5–63

work page 1985
[50]

V. E. Korepin, N. M. Bogoliubov, and A. G. Izer- gin,Quantum Inverse Scattering Method and Correla- tion Functions, Cambridge Monographs on Mathemat- ical Physics (Cambridge University Press, Cambridge, 1993)

work page 1993
[51]

Takahashi,Thermodynamics of One-Dimensional Solvable Models(Cambridge University Press, Cam- bridge, 1999)

M. Takahashi,Thermodynamics of One-Dimensional Solvable Models(Cambridge University Press, Cam- bridge, 1999)

work page 1999
[52]

Gaudin,The Bethe Wavefunction(Cambridge Uni- versity Press, Cambridge, 2014)

M. Gaudin,The Bethe Wavefunction(Cambridge Uni- versity Press, Cambridge, 2014)

work page 2014
[53]

P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Commun. Pure Appl. Math.21, 467 (1968)

work page 1968
[54]

P. P. Kulish, Factorization of the classical and the quan- tum S matrix and conservation laws, Theor. Math. Phys.26, 132 (1976)

work page 1976
[55]

L. A. Takhtadzhan and L. D. Faddeev, The quantum method of the inverse problem and the heisenberg XYZ model, Russ. Math. Surv.34, 11 (1979)

work page 1979
[56]

H. B. Thacker, Quantum inverse method for two- dimensional ice and ferroelectric lattice models, J. Math. Phys.21, 1115 (1980)

work page 1980
[57]

P. P. Kulish and E. K. Sklyanin, Quantum spectral transform method recent developments, inIntegrable Quantum Field Theories, Vol. 151, edited by J. Hi- etarinta and C. Montonen (Springer Berlin Heidelberg, Berlin, Heidelberg, 1982) pp. 61–119

work page 1982
[58]

M. G. Tetel’man, Lorentz group for two-dimensional integrable lattice systems, Sov. Phys. JETP55, 306 (1982)

work page 1982
[59]

N. Yu. Reshetikhin, A method of functional equations in the theory of exactly solvable quantum systems, Lett. Math. Phys.7, 205 (1983)

work page 1983
[60]

Sogo and M

K. Sogo and M. Wadati, Boost operator and its application to quantum gelfand-levitan equation for heisenberg-ising chain with spin one-half, Prog. Theor. Phys.69, 431 (1983)

work page 1983
[61]

E. K. Sklyanin, Quantum inverse scattering method. se- lected topics, arXiv:hep-th/9211111 (1992)

work page internal anchor Pith review Pith/arXiv arXiv 1992
[62]

M. P. Grabowski and P. Mathieu, Quantum integrals of motion for the heisenberg spin chain, Mod. Phys. Lett. A09, 2197 (1994)

work page 1994
[63]

Grabowski and P

M. Grabowski and P. Mathieu, Structure of the con- servation laws in quantum integrable spin chains with short range interactions, Ann. Phys. (N. Y.)243, 299 (1995). 20

work page 1995
[64]

L. D. Faddeev, How algebraic bethe ansatz works for integrable model, arXiv:hep-th/9605187 (1996)

work page internal anchor Pith review Pith/arXiv arXiv 1996
[65]

Hokkyo, Integrability from a single conservation law in quantum spin chains, arXiv:2508.20713 (2025)

A. Hokkyo, Integrability from a single conservation law in quantum spin chains, arXiv:2508.20713 (2025)

work page arXiv 2025
[66]

Does Quantum Chaos Explain Quantum Statistical Mechanics?

M. Srednicki, Does quantum chaos explain quantum sta- tistical mechanics?, arXiv:cond-mat/9410046 (1995)

work page internal anchor Pith review Pith/arXiv arXiv 1995
[67]

Peres,Quantum Theory: Concepts and Methods, 1st ed., Fundamental Theories of Physics No

A. Peres,Quantum Theory: Concepts and Methods, 1st ed., Fundamental Theories of Physics No. 57 (Imprint: Springer, Dordrecht, 2002)

work page 2002
[68]

Caux and J

J.-S. Caux and J. M. Maillet, Computation of dynamical correlation functions of heisenberg chains in a magnetic field, Phys. Rev. Lett.95, 077201 (2005)

work page 2005
[69]

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
[70]

Caux and J

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

work page 2011
[71]

Polkovnikov, K

A. Polkovnikov, K. Sengupta, A. Silva, and M. Ven- galattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011)

work page 2011
[72]

Steinigeweg, J

R. Steinigeweg, J. Herbrych, and P. Prelovˇ sek, Eigen- state thermalization within isolated spin-chain systems, Phys. Rev. E87, 012118 (2013)

work page 2013
[73]

Eisert, M

J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- body systems out of equilibrium, Nature Phys.11, 124 (2015)

work page 2015
[74]

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
[75]

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)

work page 2016
[76]

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
[77]

Bertini, F

B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, and M. ˇZnidariˇ c, Finite-temperature transport in one-dimensional quantum lattice models, Rev. Mod. Phys.93, 025003 (2021)

work page 2021
[78]

M. P. Grabowski and P. Mathieu, Integrability test for spin chains, J. Phys. A28, 4777 (1995)

work page 1995
[79]

Gombor and B

T. Gombor and B. Pozsgay, Integrable spin chains and cellular automata with medium range interaction, Phys. Rev. E104, 054123 (2021)

work page 2021
[80]

Shiraishi and M

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

work page arXiv 2025

Showing first 80 references.