Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model

TL;DR

This paper investigates how entanglement entropy scales in a 2D disordered quantum spin model, revealing a linear area law and a subleading logarithmic correction at criticality, linked to percolation phenomena.

Contribution

It numerically demonstrates the presence of a logarithmic correction to the entanglement entropy at the quantum critical point in a 2D random transverse field Ising model.

Findings

Entanglement entropy scales linearly with block size.

A logarithmic correction appears at the quantum critical point.

The correction relates to an underlying percolation transition.

Abstract

The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement entropy always scales linearly with the block size. However, besides this \emph{area law} contribution, we find a subleading logarithmic correction at the quantum critical point. This correction is discussed from the point of view of an underlying percolation transition, both at finite and at zero temperature.