Eigenstate thermalization and disappearance of quantum many-body scar states in weakly interacting fermion systems

Ma, Ken K. W.; Volya, A.; Yang, Kun

doi:10.1103/PhysRevB.106.214313

Eigenstate thermalization and disappearance of quantum many-body scar states in weakly interacting fermion systems

Journal Article · Fri Dec 23 00:00:00 EST 2022 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.106.214313· OSTI ID:2937460

^[1]; Volya, A. ^[2]; Yang, Kun ^[3]

National High Magnetic Field Laboratory, Tallahassee, FL (United States)
Florida State University, Tallahassee, FL (United States)
National High Magnetic Field Laboratory, Tallahassee, FL (United States); Florida State University, Tallahassee, FL (United States)

The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Eigenstates with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would be always eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a sub-volume scaling law decreases double exponentially as the system size. Furthermore, our results provide a quantitative argument for the disappearance of scar states in interacting fermion systems.

View Accepted Manuscript (DOE)

Research Organization:: Florida State Univ., Tallahassee, FL (United States); Florida State University, Tallahassee, FL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0009883

OSTI ID:: 2937460

Alternate ID(s):: OSTI ID: 2419857
OSTI ID: 1906542

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 21 Vol. 106; ISSN 2469-9950; ISSN 2469-9969

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (64)

Physics of Atomic Nuclei Zelevinsky, Vladimir; Volya, Alexander Wiley‐VCH Verlag GmbH & Co. https://doi.org/10.1002/9783527693610	book	January 2017
Embedded Random Matrix Ensembles in Quantum Physics Kota, V. K. B. Lecture Notes in Physics https://doi.org/10.1007/978-3-319-04567-2	book	January 2014
Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT He, Song; Lin, Feng-Li; Zhang, Jia-ju Journal of High Energy Physics, Vol. 2017, Issue 8 https://doi.org/10.1007/JHEP08(2017)126	journal	August 2017
Aspects of Generic Entanglement Hayden, Patrick; Leung, Debbie W.; Winter, Andreas Communications in Mathematical Physics, Vol. 265, Issue 1 https://doi.org/10.1007/s00220-006-1535-6	journal	March 2006
Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems Müller, Markus P.; Adlam, Emily; Masanes, Lluís Communications in Mathematical Physics, Vol. 340, Issue 2 https://doi.org/10.1007/s00220-015-2473-y	journal	September 2015
Quantum choas and rotational damping Åberg, S. Progress in Particle and Nuclear Physics, Vol. 28 https://doi.org/10.1016/0146-6410(92)90012-Q	journal	January 1992
Validity of random matrix theories for many-particle systems French, J. B.; Wong, S. S. M. Physics Letters B, Vol. 33, Issue 7 https://doi.org/10.1016/0370-2693(70)90213-3	journal	December 1970
Some random-matrix level and spacing distributions for fixed-particle-rank interactions French, J. B.; Wong, S. S. M. Physics Letters B, Vol. 35, Issue 1 https://doi.org/10.1016/0370-2693(71)90424-2	journal	April 1971
Two-body random hamiltonian and level density Bohigas, O.; Flores, J. Physics Letters B, Vol. 34, Issue 4 https://doi.org/10.1016/0370-2693(71)90598-3	journal	March 1971
Embedded random matrix ensembles for complexity and chaos in finite interacting particle systems Kota, V. Physics Reports, Vol. 347, Issue 3 https://doi.org/10.1016/S0370-1573(00)00113-7	journal	June 2001
The nuclear shell model as a testing ground for many-body quantum chaos Zelevinsky, Vladimir; Brown, B. Alex; Frazier, Njema Physics Reports, Vol. 276, Issue 2-3 https://doi.org/10.1016/S0370-1573(96)00007-5	journal	November 1996
Return probability: Exponential versus Gaussian decay Izrailev, F. M.; Castañeda-Mendoza, A. Physics Letters A, Vol. 350, Issue 5-6 https://doi.org/10.1016/j.physleta.2005.10.077	journal	February 2006
Quantum chaos and thermalization in isolated systems of interacting particles Borgonovi, F.; Izrailev, F. M.; Santos, L. F. Physics Reports, Vol. 626 https://doi.org/10.1016/j.physrep.2016.02.005	journal	April 2016
Thermalization and its mechanism for generic isolated quantum systems Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06838	journal	April 2008
Entanglement and the foundations of statistical mechanics Popescu, Sandu; Short, Anthony J.; Winter, Andreas Nature Physics, Vol. 2, Issue 11 https://doi.org/10.1038/nphys444	journal	October 2006
Quantum many-body scars and weak breaking of ergodicity Serbyn, Maksym; Abanin, Dmitry A.; Papić, Zlatko Nature Physics, Vol. 17, Issue 6 https://doi.org/10.1038/s41567-021-01230-2	journal	May 2021
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli Advances in Physics, Vol. 65, Issue 3 https://doi.org/10.1080/00018732.2016.1198134	journal	May 2016
The approach to thermal equilibrium in quantized chaotic systems Srednicki, Mark Journal of Physics A: Mathematical and General, Vol. 32, Issue 7 https://doi.org/10.1088/0305-4470/32/7/007	journal	January 1999
Integrability of a disordered Heisenberg spin-1/2 chain Santos, L. F. Journal of Physics A: Mathematical and General, Vol. 37, Issue 17 https://doi.org/10.1088/0305-4470/37/17/004	journal	April 2004
Eigenstate thermalization hypothesis Deutsch, Joshua M. Reports on Progress in Physics, Vol. 81, Issue 8 https://doi.org/10.1088/1361-6633/aac9f1	journal	July 2018
Quantum many-body scars and Hilbert space fragmentation: a review of exact results Moudgalya, Sanjay; Bernevig, B. Andrei; Regnault, Nicolas Reports on Progress in Physics, Vol. 85, Issue 8 https://doi.org/10.1088/1361-6633/ac73a0	journal	July 2022
Thermodynamic entropy of a many-body energy eigenstate Deutsch, J. M. New Journal of Physics, Vol. 12, Issue 7 https://doi.org/10.1088/1367-2630/12/7/075021	journal	July 2010
Thermalization in the two-body random ensemble Kota, V. K. B.; Relaño, A.; Retamosa, J. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, Issue 10 https://doi.org/10.1088/1742-5468/2011/10/P10028	journal	October 2011
Volume-Law Entanglement Entropy of Typical Pure Quantum States Bianchi, Eugenio; Hackl, Lucas; Kieburg, Mario PRX Quantum, Vol. 3, Issue 3 https://doi.org/10.1103/PRXQuantum.3.030201	journal	July 2022
Quantum statistical mechanics in a closed system Deutsch, J. M. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.2046	journal	February 1991
Entanglement of subspaces in terms of entanglement of superpositions Gour, Gilad; Roy, Aidan Physical Review A, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevA.77.012336	journal	January 2008
Exact three-colored quantum scars from geometric frustration Lee, Kyungmin; Melendrez, Ronald; Pal, Arijeet Physical Review B, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevB.101.241111	journal	June 2020
Exact many-body scars and their stability in constrained quantum chains Surace, Federica Maria; Votto, Matteo; Lazo, Eduardo Gonzalez Physical Review B, Vol. 103, Issue 10 https://doi.org/10.1103/PhysRevB.103.104302	journal	March 2021
Stability of scar states in the two-dimensional PXP model against random disorder Huang, Ke; Wang, Yu; Li, Xiao Physical Review B, Vol. 104, Issue 21 https://doi.org/10.1103/PhysRevB.104.214305	journal	December 2021
Onset of many-body quantum chaos due to breaking integrability Bulchandani, Vir B.; Huse, David A.; Gopalakrishnan, Sarang Physical Review B, Vol. 105, Issue 21 https://doi.org/10.1103/PhysRevB.105.214308	journal	June 2022
Rainbow scars: From area to volume law Langlett, Christopher M.; Yang, Zhi-Cheng; Wildeboer, Julia Physical Review B, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevB.105.L060301	journal	February 2022
Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems Ma, Ken K. W.; Yang, Kun Physical Review B, Vol. 106, Issue 3 https://doi.org/10.1103/PhysRevB.106.035143	journal	July 2022
Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions Tamura, Kensuke; Katsura, Hosho Physical Review B, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevB.106.144306	journal	October 2022
Crossover from Poisson to Wigner-Dyson level statistics in spin chains with integrability breaking Rabson, D. A.; Narozhny, B. N.; Millis, A. J. Physical Review B, Vol. 69, Issue 5 https://doi.org/10.1103/PhysRevB.69.054403	journal	February 2004
Universal power law in crossover from integrability to quantum chaos Modak, Ranjan; Mukerjee, Subroto; Ramaswamy, Sriram Physical Review B, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevB.90.075152	journal	August 2014
Entanglement entropy scaling laws and eigenstate typicality in free fermion systems Lai, Hsin-Hua; Yang, Kun Physical Review B, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevB.91.081110	journal	February 2015
Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations Turner, C. J.; Michailidis, A. A.; Abanin, D. A. Physical Review B, Vol. 98, Issue 15 https://doi.org/10.1103/PhysRevB.98.155134	journal	October 2018
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Correlations within eigenvectors and transition amplitudes in the two-body random interaction model Flambaum, V. V.; Gribakin, G. F.; Izrailev, F. M. Physical Review E, Vol. 53, Issue 6 https://doi.org/10.1103/PhysRevE.53.5729	journal	June 1996
Towards a statistical theory of finite Fermi systems and compound states: Random two-body interaction approach Flambaum, V. V.; Izrailev, F. M.; Casati, G. Physical Review E, Vol. 54, Issue 2 https://doi.org/10.1103/PhysRevE.54.2136	journal	August 1996
Distribution of occupation numbers in finite Fermi systemsand role of interaction in chaos and thermalization Flambaum, V. V.; Izrailev, F. M. Physical Review E, Vol. 55, Issue 1 https://doi.org/10.1103/PhysRevE.55.R13	journal	January 1997
Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates Flambaum, V. V.; Izrailev, F. M. Physical Review E, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevE.56.5144	journal	November 1997
Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems Angom, D.; Ghosh, S.; Kota, V. K. B. Physical Review E, Vol. 70, Issue 1 https://doi.org/10.1103/PhysRevE.70.016209	journal	July 2004
Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization Santos, Lea F.; Rigol, Marcos Physical Review E, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevE.81.036206	journal	March 2010
Onset of chaos and relaxation in isolated systems of interacting spins: Energy shell approach Santos, L. F.; Borgonovi, F.; Izrailev, F. M. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.036209	journal	March 2012
Weak and strong typicality in quantum systems Santos, Lea F.; Polkovnikov, Anatoli; Rigol, Marcos Physical Review E, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevE.86.010102	journal	July 2012
Microscopic origin of thermodynamic entropy in isolated systems Deutsch, J. M.; Li, Haibin; Sharma, Auditya Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.042135	journal	April 2013
Testing whether all eigenstates obey the eigenstate thermalization hypothesis Kim, Hyungwon; Ikeda, Tatsuhiko N.; Huse, David A. Physical Review E, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevE.90.052105	journal	November 2014
Temperature of a single chaotic eigenstate Borgonovi, Fausto; Mattiotti, Francesco; Izrailev, Felix M. Physical Review E, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevE.95.042135	journal	April 2017
Subsystem eigenstate thermalization hypothesis Dymarsky, Anatoly; Lashkari, Nima; Liu, Hong Physical Review E, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevE.97.012140	journal	January 2018
Hidden thermal structure in Fock space Tian, Chushun; Yang, Kun; Fang, Ping Physical Review E, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevE.98.060103	journal	December 2018
Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems Biroli, Giulio; Kollath, Corinna; Läuchli, Andreas M. Physical Review Letters, Vol. 105, Issue 25 https://doi.org/10.1103/PhysRevLett.105.250401	journal	December 2010
Chaos and Statistical Relaxation in Quantum Systems of Interacting Particles Santos, L. F.; Borgonovi, F.; Izrailev, F. M. Physical Review Letters, Vol. 108, Issue 9 https://doi.org/10.1103/PhysRevLett.108.094102	journal	March 2012
Eigenstate Thermalization in a Locally Perturbed Integrable System Brenes, Marlon; LeBlond, Tyler; Goold, John Physical Review Letters, Vol. 125, Issue 7 https://doi.org/10.1103/PhysRevLett.125.070605	journal	August 2020
Onset of chaos in rapidly rotating nuclei Åberg, Sven Physical Review Letters, Vol. 64, Issue 26 https://doi.org/10.1103/PhysRevLett.64.3119	journal	June 1990
Quasiparticle Lifetime in a Finite System: A Nonperturbative Approach Altshuler, Boris L.; Gefen, Yuval; Kamenev, Alex Physical Review Letters, Vol. 78, Issue 14 https://doi.org/10.1103/PhysRevLett.78.2803	journal	April 1997
Emergence of Quantum Chaos in Finite Interacting Fermi Systems Jacquod, Ph.; Shepelyansky, D. L. Physical Review Letters, Vol. 79, Issue 10 https://doi.org/10.1103/PhysRevLett.79.1837	journal	September 1997
Breit-Wigner Width and Inverse Participation Ratio in Finite Interacting Fermi Systems Georgeot, B.; Shepelyansky, D. L. Physical Review Letters, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevLett.79.4365	journal	December 1997
Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions Jacquod, Philippe; Varga, Imre Physical Review Letters, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevLett.89.134101	journal	September 2002
Canonical Typicality Goldstein, Sheldon; Lebowitz, Joel L.; Tumulka, Roderich Physical Review Letters, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevLett.96.050403	journal	February 2006
Entanglement of Superpositions Linden, Noah; Popescu, Sandu; Smolin, John A. Physical Review Letters, Vol. 97, Issue 10 https://doi.org/10.1103/PhysRevLett.97.100502	journal	September 2006
Slow thermalization of exact quantum many-body scar states under perturbations Lin, Cheng-Ju; Chandran, Anushya; Motrunich, Olexei I. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033044	journal	July 2020
Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos Pandey, Mohit; Claeys, Pieter W.; Campbell, David K. Physical Review X, Vol. 10, Issue 4 https://doi.org/10.1103/PhysRevX.10.041017	journal	October 2020
Does a Single Eigenstate Encode the Full Hamiltonian? Garrison, James R.; Grover, Tarun Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021026	journal	April 2018

Similar Records

Lindblad many-body scars

Journal Article · Tue Feb 10 19:00:00 EST 2026 · Physical Review. E · OSTI ID:3021130

Quantum many-body scars from Einstein-Podolsky-Rosen states in bilayer systems

Journal Article · Sun Nov 27 19:00:00 EST 2022 · Physical Review. B · OSTI ID:2420919

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Eigenstate thermalization
Entanglement entropy
Quantum complexity
Quantum entanglement
Quantum scars
Quantum statistical mechanics
entanglement entropy
quantum entanglement
quantum scars
quantum statistical mechanics

Eigenstate thermalization and disappearance of quantum many-body scar states in weakly interacting fermion systems

Citation Formats

References (64)

Similar Records

Related Subjects