Universal entanglement entropy in 2D conformal quantum critical points

TL;DR

This paper investigates the universal finite part of entanglement entropy in 2D conformal quantum critical systems, linking it to boundary conformal field theory and revealing universal features across various models.

Contribution

It demonstrates that the universal finite entanglement entropy can be computed from the conformal structure of the wave function, unifying different models under a common framework.

Findings

Universal finite entanglement entropy exists for 2D conformal quantum critical points.

The universal term is computable via boundary conformal field theory methods.

Results apply to models like quantum dimer, loop models, and gauge theories.

Abstract

We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory.