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

2018/06/30 by Sanjay Moudgalya, Nicolas Regnault, B. Andrei Bernevig · 10 citations
Mathematics · Physics and Astronomy · #Density matrix #Eigenvalues and eigenvectors #Exact solutions in general relativity #Excited state #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #cond-mat.stat-mech #cond-mat.str-el #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevb.98.235156

published as Phys. Rev. B 98, 235156 (2018) · 44 pages, 6 figures v2: References added

arxiv created 2018/07/10 · openalex created_date 2018/07/10 · openalex publication_date 2018/12/27 · arxiv updated 2018/12/31 · openalex updated_date 2026/08/06

Abstract

Here, the authors develop a general formalism to analytically compute the entanglement spectra of exact excited states and use it to obtain the entanglement spectra of the infinite tower of states of the spin-S AKLT models, which are the first analytical examples of what are now called quantum many-body scars. Located in the bulk of the spectrum, these states have a subthermal entanglement entropy, showing for the first time the violation of the strong eigenstate thermalization hypothesis (ETH) in a well-known translation-invariant nonintegrable model.

Citations

• Exact Excited States of Non-Integrable Models
• Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
• Detection of symmetry-protected topological phases in one dimension
• From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
• Matrix product representations for all valence bond states
• ENTANGLEMENT IN VALENCE-BOND-SOLID STATES
• Many-Body Localization in a Disordered Quantum Ising Chain
• Many-body localization in the HeisenbergXXZmagnet in a random field
• Finite automata for caching in matrix product algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Chaos and Quantum Thermalization
• Entanglement spectrum of a topological phase in one dimension
• Entanglement in a Valence-Bond Solid State
• Matrix product states represent ground states faithfully
• Post-matrix product state methods: To tangent space and beyond
• Quantum statistical mechanics in a closed system
• Exact analysis of entanglement in gapped quantum spin chains
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• String order and symmetries in quantum spin lattices
• Classification of gapped symmetric phases in one-dimensional spin systems
• The density-matrix renormalization group in the age of matrix product states
• Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states
• Entanglement content of quantum particle excitations. Part I. Free field theory

Cited by

• Fibonacci many-body scars in a decorated Rule-54 quantum cellular automaton
• Quantum Many-Body Scars beyond the PXP Model in Rydberg Simulators
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
• Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space
• Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
• ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics
• Liouvillian Spectral Transition in Noisy Quantum Many-Body Scars
• Statistical localization: From strong fragmentation to strong edge modes
• Restoring coherence via aperiodic drives in a many-body quantum system
• Localized dynamics following a quantum quench in a non-integrable system: an example on the sawtooth ladder

Related

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