On the entanglement across a cubic interface in 3+1 dimensions

TL;DR

This paper investigates the entanglement entropy in the 3+1 dimensional transverse-field Ising model, revealing positive corner contributions and a sharp cusp at the critical point, with results aligning with conformal field theory predictions.

Contribution

It provides the first detailed series expansion analysis of entanglement entropies across cubic interfaces in 3+1 dimensions, including corner effects and their conformal field theory correspondence.

Findings

Corner contributions are positive in 3D.

Series expansions converge up to the critical point.

Logarithmic divergence coefficients match CFT results.

Abstract

We calculate the area, edge and corner Renyi entanglement entropies in the ground state of the transverse-field Ising model, on a simple-cubic lattice, by high-field and low-field series expansions. We find that while the area term is positive and the line term is negative as required by strong subadditivity, the corner contributions are positive in 3-dimensions. Analysis of the series suggests that the expansions converge up to the physical critical point from both sides. The leading area-law Renyi entropies match nicely from the high and low field expansions at the critical point, forming a sharp cusp there. We calculate the coefficients of the logarithmic divergence associated with the corner entropy and compare them with conformal field theory results with smooth interfaces and find a striking correspondence.