A generalized volume law for entanglement entropy on the fuzzy sphere

TL;DR

This paper explores how entanglement entropy behaves in a scalar field theory on the fuzzy sphere, revealing a transition from a volume law to an area law as the system parameters change, using matrix models and Monte Carlo simulations.

Contribution

It introduces a generalized volume law for entanglement entropy on the fuzzy sphere and analyzes the transition to the area law through numerical simulations.

Findings

Entanglement entropy in the free case scales with the square of the boundary area.

A transition from a generalized volume law to an area law is observed in the interacting case.

The behavior is explained by the matrix regularization of the theory.

Abstract

We investigate entanglement entropy in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model. In our previous study, we confirmed that entanglement entropy in the free case is proportional to the square of the boundary area of a focused region. Here we argue that this behavior of entanglement entropy can be understood by the fact that the theory is regularized by matrices, and further examine the dependence of entanglement entropy on the matrix size. In the interacting case, by performing Monte Carlo simulations, we observe a transition from a generalized volume law, which is obtained by integrating the square of area law, to the square of area law.