Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line

TL;DR

This paper investigates the entanglement entropy of the 2D Edwards-Anderson model along the Nishimori line, revealing critical behavior and estimating the central charge using TEBD and transfer matrix methods.

Contribution

It introduces a classical analogue of entanglement entropy for the 2D EA model and analyzes its critical behavior at the Nishimori point using advanced numerical techniques.

Findings

Entanglement entropy shows critical singularity at the Nishimori point.

The boundary state has an estimated central charge.

The TEBD method effectively computes boundary spin distributions.

Abstract

A classical analogue of the entanglement entropy is calculated on the system boundary of the two-dimensional Edwards-Anderson model, where the nearest-neighbor interaction is stochastically chosen from +J and -J. The boundary spin distribution is obtained by means of the time-evolving block decimation (TEBD) method, where the random ensemble is created from the successive multiplications of position-dependent transfer matrices, whose width is up to N = 300. The random average of the entanglement entropy is calculated on the Nishimori line, and it is confirmed that the entanglement entropy shows critical singularity at the Nishimori point. The central charge of the boundary state is estimated.