Two-cylinder entanglement entropy under a twist

TL;DR

This paper investigates the universal entanglement entropy of various scale-invariant theories on tori with twisted boundary conditions, revealing how shape and mass deformations influence EE and uncovering non-monotonic RG flow behaviors.

Contribution

It provides analytical and numerical results for the entanglement entropy of multiple conformal and non-conformal theories on tori with twists, highlighting shape dependence and RG flow effects.

Findings

Shape dependence distinguishes different theories.

Non-monotonic behavior of EE under RG flow.

Universal EE captures effects of twists and mass deformations.

Abstract

We study the von Neumann and R\'enyi entanglement entropy (EE) of scale-invariant theories defined on tori in 2+1 and 3+1 spacetime dimensions. We focus on spatial bi-partitions of the torus into two cylinders, and allow for twisted boundary conditions along the non-contractible cycles. Various analytical and numerical results are obtained for the universal EE of the relativistic boson and Dirac fermion conformal field theories (CFTs), and for the fermionic quadratic band touching and the boson with $z=2$ Lifshitz scaling. The shape dependence of the EE clearly distinguishes these theories, although intriguing similarities are found in certain limits. We also study the evolution of the EE when a mass is introduced to detune the system from its scale-invariant point, by employing a renormalized EE that goes beyond a naive subtraction of the area law. In certain cases we find non-monotonic behavior of the torus EE under RG flow, which distinguishes it from the EE of a disk.