Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model

Abstract

We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$\frac{1}{2}$ XYZ chain away from and at special lines with $U(1)$ symmetry and supersymmetry. We universally find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that of quantum-chaotic interacting models. At the supersymmetric point, we resolve the effect that degeneracies have on the computed averages. We further find that the normalized standard deviation of the eigenstate entanglement entropy decays polynomially with increasing system size, which we contrast to the exponential decay in quantum-chaotic interacting models. Our results provide state-of-the art numerical evidence that integrability in spin-$\frac{1}{2}$ chains reduces the average, and increases the standard deviation, of the entanglement entropy of highly excited energy eigenstates when compared to those in quantum-chaotic interacting models.

References in corpus (36)

• Area laws for the entanglement entropy - a review
• Nonequilibrium dynamics of closed interacting quantum systems
• Topological entanglement entropy
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Entanglement entropy and conformal field theory
• Average Entropy of a Subsystem
• Identifying Topological Order by Entanglement Entropy
• Finite-size scaling of eigenstate thermalization
• Does a single eigenstate encode the full Hamiltonian?
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Subsystem ETH
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Entanglement and matrix elements of observables in interacting integrable systems
• Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
• Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
• Scattering and Thermodynamics of Fractionally-Charged Supersymmetric Solitons
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Lattice fermion models with supersymmetry
• Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Two-component Structure in the Entanglement Spectrum of Highly Excited States
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• The Page Curve for Fermionic Gaussian States
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Eigenstate thermalization hypothesis and integrals of motion
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Spin chains with dynamical lattice supersymmetry
• The eight-vertex model and lattice supersymmetry
• Exact and simple results for the XYZ and strongly interacting fermion chains
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Tight-binding billiards
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

Cited by in corpus (6)

• Normal weak eigenstate thermalization
• Non-abelian symmetry-resolved entanglement entropy
• Weak ergodicity breaking with isolated integrable sectors
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Localization transitions in quadratic systems without quantum chaos