Entanglement entropy of excited states

TL;DR

This paper investigates the entanglement entropy in excited states of spin chains, revealing two main classes with distinct scaling behaviors linked to excitation properties and Hamiltonian locality.

Contribution

It introduces a numerical method based on algebraic Bethe Ansatz for the XXZ model and classifies excited states by their entanglement entropy scaling.

Findings

Identifies logarithmic and extensive entanglement entropy behaviors.

Links entanglement scaling to excitation properties and Hamiltonian locality.

Provides finite size scaling analysis.

Abstract

We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin-chain. For the latter, we developed a numerical application of algebraic Bethe Ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as ground state. We also provide several details of the finite size scaling.