Universal eigenstate entanglement of chaotic local Hamiltonians

TL;DR

This work conjectures a universal formula for the average eigenstate entanglement entropy in chaotic local Hamiltonians, supported by analytical arguments and numerical simulations, extending to a fraction of eigenstates in the spectrum.

Contribution

It introduces a universal formula for eigenstate entanglement entropy in chaotic systems and extends the analysis to a subset of eigenstates, supported by numerical evidence.

Findings

Universal eigenstate entanglement entropy formula proposed

Numerical simulations support the conjectured formula

Extension to middle spectrum eigenstates demonstrated

Abstract

This arXiv repository is a bundle of two closely related papers. Abstract of the first paper: In systems governed by "chaotic" local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average entanglement entropy of all eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations. Abstract of the second paper: In systems governed by chaotic local Hamiltonians, the first paper conjectured the universality of the average entanglement entropy of all eigenstates by proposing an exact formula for its dependence on the subsystem size. In this note, I extend this result to the average entanglement entropy of a constant fraction of eigenstates in the middle of the energy spectrum. The generalized formula is supported by numerical simulations of various chaotic spin chains.