Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis
Abstract
We obtain multiple exact results on the entanglement of the exact excited states of nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018). We first discuss a general formalism to analytically compute the entanglement spectra of exact excited states using matrix product states and matrix product operators and illustrate the method by reproducing a general result on single-mode excitations. We then apply this technique to analytically obtain the entanglement spectra of the infinite tower of states of the spin-S AKLT models in the zero and finite energy density limits. We show that in the zero energy density limit, the entanglement spectra of the tower of states are multiple shifted copies of the ground-state entanglement spectrum in the thermodynamic limit. We show that such a resemblance is destroyed at any nonzero energy density. Furthermore, the entanglement entropy S of the states of the tower that are in the bulk of the spectrum is subthermal S ∝ log L, as opposed to a volume law S ∝ L, thus indicating a violation of the strong eigenstate thermalization hypothesis (ETH). These states are examples of what are now called many-body scars. Lastly, we analytically study the finite-size effects and symmetry-protected degeneraciesmore »
- Authors:
-
- Princeton Univ., NJ (United States)
- Univ. Paris Diderot (France)
- Princeton Univ., NJ (United States); Freie Univ. Berlin (Germany); Max Planck Inst. of Microstructure Physics, Halle (Germany); Donostia International Physics Center (Spain); Sorbonne Univ., Paris (France); Univ. Paris Diderot (France)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1612430
- Alternate Identifier(s):
- OSTI ID: 1488978
- Grant/Contract Number:
- SC0016239; de-sc0016239
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; 1-dimensional spin chains; Discrete symmetries in condensed matter; Exact solutions for many-body systems; Projective symmetries; Spin lattice models; Symmetries; Symmetries in condensed matter; Tensor network methods
Citation Formats
Moudgalya, Sanjay, Regnault, Nicolas, and Bernevig, B. Andrei. Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis. United States: N. p., 2018.
Web. doi:10.1103/physrevb.98.235156.
Moudgalya, Sanjay, Regnault, Nicolas, & Bernevig, B. Andrei. Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis. United States. https://doi.org/10.1103/physrevb.98.235156
Moudgalya, Sanjay, Regnault, Nicolas, and Bernevig, B. Andrei. Thu .
"Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis". United States. https://doi.org/10.1103/physrevb.98.235156. https://www.osti.gov/servlets/purl/1612430.
@article{osti_1612430,
title = {Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis},
author = {Moudgalya, Sanjay and Regnault, Nicolas and Bernevig, B. Andrei},
abstractNote = {We obtain multiple exact results on the entanglement of the exact excited states of nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018). We first discuss a general formalism to analytically compute the entanglement spectra of exact excited states using matrix product states and matrix product operators and illustrate the method by reproducing a general result on single-mode excitations. We then apply this technique to analytically obtain the entanglement spectra of the infinite tower of states of the spin-S AKLT models in the zero and finite energy density limits. We show that in the zero energy density limit, the entanglement spectra of the tower of states are multiple shifted copies of the ground-state entanglement spectrum in the thermodynamic limit. We show that such a resemblance is destroyed at any nonzero energy density. Furthermore, the entanglement entropy S of the states of the tower that are in the bulk of the spectrum is subthermal S ∝ log L, as opposed to a volume law S ∝ L, thus indicating a violation of the strong eigenstate thermalization hypothesis (ETH). These states are examples of what are now called many-body scars. Lastly, we analytically study the finite-size effects and symmetry-protected degeneracies in the entanglement spectra of the excited states, extending the existing theory.},
doi = {10.1103/physrevb.98.235156},
journal = {Physical Review. B},
number = 23,
volume = 98,
place = {United States},
year = {Thu Dec 27 00:00:00 EST 2018},
month = {Thu Dec 27 00:00:00 EST 2018}
}
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Signatures of integrability in the dynamics of Rydberg-blockaded chains
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- Khemani, Vedika; Laumann, Chris R.; Chandran, Anushya
- Physical Review B, Vol. 99, Issue 16
Nonthermal States Arising from Confinement in One and Two Dimensions
journal, April 2019
- James, Andrew J. A.; Konik, Robert M.; Robinson, Neil J.
- Physical Review Letters, Vol. 122, Issue 13
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
journal, April 2019
- Lin, Cheng-Ju; Motrunich, Olexei I.
- Physical Review Letters, Vol. 122, Issue 17
Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model
journal, July 2019
- Iadecola, Thomas; Žnidarič, Marko
- Physical Review Letters, Vol. 123, Issue 3
Dynamical Scar States in Driven Fracton Systems
journal, September 2019
- Pai, Shriya; Pretko, Michael
- Physical Review Letters, Vol. 123, Issue 13
Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis
journal, January 2020
- Mierzejewski, Marcin; Vidmar, Lev
- Physical Review Letters, Vol. 124, Issue 4
Entanglement-ergodic quantum systems equilibrate exponentially well
text, January 2019
- Wilming, H.; Goihl, M.; Roth, I.
- Freie Universität Berlin
Topological many-body scar states in dimensions one, two, and three
text, January 2019
- Ok, Seulgi; Choo, Kenny; Mudry, Christopher
- University of Zurich
Entanglement-Ergodic Quantum Systems Equilibrate Exponentially Well
journal, November 2019
- Wilming, H.; Goihl, M.; Roth, I.
- Physical Review Letters, Vol. 123, Issue 20
Exact Excited States of Non-Integrable Models
text, January 2017
- Moudgalya, Sanjay; Rachel, Stephan; Bernevig, B. Andrei
- arXiv
Signatures of integrability in the dynamics of Rydberg-blockaded chains
text, January 2018
- Khemani, Vedika; Laumann, Chris R.; Chandran, Anushya
- arXiv
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
text, January 2018
- Lin, Cheng-Ju; Motrunich, Olexei I.
- arXiv
Emergent SU(2) dynamics and perfect quantum many-body scars
text, January 2018
- Choi, Soonwon; Turner, Christopher J.; Pichler, Hannes
- arXiv
Dynamical scar states in driven fracton systems
text, January 2019
- Pai, Shriya; Pretko, Michael
- arXiv
Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
text, January 2019
- Sala, Pablo; Rakovszky, Tibor; Verresen, Ruben
- arXiv
Quantum many-body scars and weak breaking of ergodicity
journal, May 2021
- Serbyn, Maksym; Abanin, Dmitry A.; Papić, Zlatko
- Nature Physics, Vol. 17, Issue 6
Exact three-colored quantum scars from geometric frustration
journal, June 2020
- Lee, Kyungmin; Melendrez, Ronald; Pal, Arijeet
- Physical Review B, Vol. 101, Issue 24
Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
journal, January 2022
- Haque, Masudul; McClarty, Paul A.; Khaymovich, Ivan M.
- Physical Review E, Vol. 105, Issue 1
Many-Body Scars as a Group Invariant Sector of Hilbert Space
journal, December 2020
- Pakrouski, K.; Pallegar, P. N.; Popov, F. K.
- Physical Review Letters, Vol. 125, Issue 23
Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model
journal, May 2021
- Desaules, Jean-Yves; Hudomal, Ana; Turner, Christopher J.
- Physical Review Letters, Vol. 126, Issue 21
Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse
journal, August 2022
- Shinjo, Kazuya; Sota, Shigetoshi; Tohyama, Takami
- Physical Review Research, Vol. 4, Issue 3
Connection between quantum-many-body scars and the AKLT model from the viewpoint of embedded Hamiltonians
text, January 2019
- Shiraishi, Naoto
- arXiv
Lack of thermalization in (1+1)-d QCD at large $N_c$
preprint, January 2019
- Cubero, Axel Cortés; Robinson, Neil J.
- arXiv
Interrelations among frustration-free models via Witten's conjugation
text, January 2020
- Wouters, Jurriaan; Katsura, Hosho; Schuricht, Dirk
- arXiv
Undecidability of the fate of relaxation in one-dimensional quantum systems
text, January 2020
- Shiraishi, Naoto; Matsumoto, Keiji
- arXiv
Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
text, January 2021
- Gorsky, Alexander; Valba, Olga
- arXiv
Prominent quantum many-body scars in a truncated Schwinger model
text, January 2022
- Desaules, Jean-Yves; Hudomal, Ana; Banerjee, Debasish
- arXiv