Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains

TL;DR

This paper investigates universal logarithmic terms in entanglement and Shannon entropies at 2D quantum critical points, revealing model-specific behaviors and boundary condition effects in spin chains and conformal field theories.

Contribution

It demonstrates the presence of universal logarithmic terms in entanglement and Shannon entropies at 2D quantum critical points and analyzes their dependence on boundary conditions and model specifics.

Findings

Logarithmic terms in Shannon entropy of the XXZ chain imply universal coefficients.

Logarithmic behavior in the transverse-field Ising model's Shannon entropy depends on Rènyi index.

Boundary conditions significantly influence the singularities in entanglement entropy at critical points.

Abstract

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient $\pm 0.25$. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on replica or R\'enyi index resulting from flows to different boundary conditions at the entanglement cut.