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Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis

Journal Article · · Physical Review. B
 [1];  [2];  [3]
  1. Princeton Univ., NJ (United States); DOE/OSTI
  2. Univ. Paris Diderot (France)
  3. 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)
+ Show Author Affiliations
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.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0016239
OSTI ID:
1612430
Alternate ID(s):
OSTI ID: 1488978
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 23 Vol. 98; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (41)

Quantum many-body scars and weak breaking of ergodicity journal May 2021
Exact three-colored quantum scars from geometric frustration journal June 2020
Signatures of rare states and thermalization in a theory with confinement journal May 2019
Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles journal January 2022
Many-Body Scars as a Group Invariant Sector of Hilbert Space journal December 2020
Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model journal May 2021
Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse journal August 2022
Connection between quantum-many-body scars and the AKLT model from the viewpoint of embedded Hamiltonians text January 2019
Lack of thermalization in (1+1)-d QCD at large $N_c$ preprint January 2019
Interrelations among frustration-free models via Witten's conjugation text January 2020
Undecidability of the fate of relaxation in one-dimensional quantum systems text January 2020
Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs text January 2021
Prominent quantum many-body scars in a truncated Schwinger model text January 2022
Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians journal August 2019
Nonthermal States Arising from Confinement in One and Two Dimensions journal April 2019
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain journal April 2019
Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model journal July 2019
Quantum many-body scars from magnon condensation journal November 2019
Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization journal December 2019
Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals journal January 2020
Exact excited states of nonintegrable models journal December 2018
Operator spreading in quantum maps journal March 2019
Signatures of integrability in the dynamics of Rydberg-blockaded chains journal April 2019
Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars journal June 2019
Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models journal July 2019
Dynamical Scar States in Driven Fracton Systems journal September 2019
Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 X Y Magnets journal October 2019
Entanglement-Ergodic Quantum Systems Equilibrate Exponentially Well journal November 2019
Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis journal January 2020
Topological many-body scar states in dimensions one, two, and three journal December 2019
Fractons from confinement in one dimension journal January 2020
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians journal February 2020
Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space journal March 2020
Entanglement-ergodic quantum systems equilibrate exponentially well text January 2019
Exact Excited States of Non-Integrable Models text January 2017
Signatures of integrability in the dynamics of Rydberg-blockaded chains text January 2018
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain text January 2018
Emergent SU(2) dynamics and perfect quantum many-body scars text January 2018
Dynamical scar states in driven fracton systems text January 2019
Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians text January 2019
Topological many-body scar states in dimensions one, two, and three text January 2019

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