Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model

TL;DR

This paper investigates the entanglement entropy of eigenstates in the 1D quantum Ising model, revealing universal volume-law scaling and a critical point signature in subleading terms.

Contribution

It uncovers universal volume-law behavior and criticality signatures in the average entanglement entropy of excited eigenstates in the quantum Ising model.

Findings

Volume-law scaling of entanglement entropy is universal for quadratic models.

Subleading constant term peaks at the quantum critical point.

Critical field can be identified from entanglement entropy corrections.

Abstract

Much has been learned about universal properties of entanglement entropies in ground states of quantum many-body lattice systems. Here we unveil universal properties of the average bipartite entanglement entropy of eigenstates of the paradigmatic quantum Ising model in one dimension. The leading term exhibits a volume-law scaling that we argue is universal for translationally invariant quadratic models. The subleading term is constant at the critical field for the quantum phase transition and vanishes otherwise (in the thermodynamic limit), i.e., the critical field can be identified from subleading corrections to the average (over all eigenstates) entanglement entropy.