Entanglement Entropy of Systems with Spontaneously Broken Continuous Symmetry

TL;DR

This paper investigates how spontaneous continuous symmetry breaking affects entanglement entropy, revealing a universal logarithmic correction linked to Goldstone modes, supported by analytical calculations and Monte Carlo simulations.

Contribution

It provides a universal formula for the logarithmic correction to entanglement entropy due to Goldstone modes in systems with broken continuous symmetry.

Findings

Logarithmic divergence in entanglement entropy proportional to N_G(d-1)/2.

Presence of a 'tower of states' structure in the entanglement spectrum.

Confirmation of theoretical predictions through Monte Carlo simulations.

Abstract

We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges logarithmically with the subsystem size in agreement with the Monte Carlo simulations of A. Kallin et. al. (Phys. Rev. B 84, 165134 (2011)). The coefficient of the logarithm is a universal number given simply by $N_G (d-1)/2$, where $N_G$ is the number of Goldstone modes and $d$ is the spatial dimension. This term is present even when the subsystem boundary is straight and contains no corners, and its origin lies in the interplay of Goldstone modes and restoration of symmetry in a finite volume. We also compute the "low-energy" part of the entanglement spectrum and show that it has the same characteristic "tower of states" form as the physical low-energy spectrum obtained when a system with spontaneously broken continuous symmetry is placed in a finite volume.