Entanglement Entropy of Periodic Sublattices

TL;DR

This paper provides exact calculations of entanglement entropy for Gaussian lattice systems with periodic sublattices, revealing extensive growth and behavior in various limits, applicable to both vacuum and thermal states.

Contribution

It introduces a method to compute entanglement entropy exactly for periodic sublattices in Gaussian systems, including at nonzero temperatures, and analyzes its behavior in different physical limits.

Findings

Entanglement entropy grows extensively for large sublattices.

Exact analytic expressions for EE are derived in various limits.

EE behavior is characterized in both massless and continuum limits.

Abstract

We study the entanglement entropy (EE) of Gaussian systems on a lattice with periodic boundary conditions, both in the vacuum and at nonzero temperatures. By restricting the reduced subsystem to periodic sublattices, we can compute the entanglement spectrum and EE exactly. We illustrate this for a free (1+1)-dimensional massive scalar field at a fixed temperature. Consistent with previous literature, we demonstrate that for a sufficiently large periodic sublattice the EE grows extensively, even in the vacuum. Furthermore, the analytic expression for the EE allows us probe its behavior both in the massless limit and in the continuum limit at any temperature.