Universal entanglement entropy in 2D conformal quantum critical points

TL;DR

This work reveals that 2D conformal quantum critical points with scale-invariant wave functions possess a universal finite contribution to the entanglement entropy, γ_QCP, when considering large simply connected subregions with smooth boundaries. By leveraging the replica trick and boundary CFT, the authors connect γ_QCP to the modular S-matrix and Affleck-Ludwig boundary entropy of the underlying RCFTs, providing explicit expressions for the quantum Lifshitz universality class and a general RCFT framework. They apply the theory to quantum Lifshitz models, quantum dimer/eight-vertex models, quantum loop/net models, and the 2D Ising RCFT, obtaining concrete γ_QCP values that depend on geometry, boundary conditions, and RCFT data. The findings distinguish γ_QCP from topological entanglement entropy while revealing structural parallels, highlighting a path to compute entanglement fingerprints of a broad class of 2D critical quantum states via boundary CFT data.

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.

Figures (3)

• Figure 1: Cylinder
• Figure 2: Torus
• Figure 3: Disk