Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models

TL;DR

This paper investigates the entanglement entropy in random transverse-field Ising models across 2d, 3d, and 4d, revealing universal logarithmic corner contributions at criticality through numerical strong disorder renormalization group analysis.

Contribution

It demonstrates the universality of corner-induced logarithmic terms in entanglement entropy across multiple dimensions at critical points.

Findings

Area law holds in all cases.

Corner contributions are logarithmically divergent at criticality.

Prefactors are universal, independent of disorder form.

Abstract

The entanglement entropy of the random transverse-field Ising model is calculated by a numerical implementation of the asymptotically exact strong disorder renormalization group method in 2d, 3d and 4d hypercubic lattices for different shapes of the subregion. We find that the area law is always satisfied, but there are analytic corrections due to E-dimensional edges (1<=E<=d-2). More interesting is the contribution arising from corners, which is logarithmically divergent at the critical point and its prefactor in a given dimension is universal, i.e. independent of the form of disorder.