Detecting Goldstone Modes with Entanglement Entropy

TL;DR

This paper confirms that systems with spontaneous continuous symmetry breaking exhibit a universal logarithmic contribution to entanglement entropy, which can be used to identify Goldstone modes through quantum Monte Carlo simulations.

Contribution

The study provides numerical evidence for the universal logarithmic term in entanglement entropy linked to Goldstone modes, validating analytical predictions.

Findings

Logarithmic term in entanglement entropy identified

Single Goldstone mode detected via entropy coefficient

Universal geometric constant matches free bosonic field theory

Abstract

In the face of mounting numerical evidence, Metlitski and Grover [arXiv:1112.5166] have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a sub-leading contribution to the entanglement entropy that diverges logarithmically with system size. They predict that the coefficient of this log is a universal quantity that depends on the number of Goldstone modes. In this paper, we confirm the presence of this log term through quantum Monte Carlo calculations of the second R\'enyi entropy on the spin 1/2 XY model. Devising an algorithm to facilitate convergence of entropy data at extremely low temperatures, we demonstrate that the single Goldstone mode in the ground state can be identified through the coefficient of the log term. Furthermore, our simulation accuracy allows us to obtain an additional geometric constant additive to the R\'enyi entropy, that matches a predicted fully-universal form obtained from a free bosonic field theory with no adjustable parameters.