Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point

TL;DR

This paper investigates the entanglement entropy in two-dimensional quantum Lifshitz critical points, addressing subtle issues in boundary conformal field theory and confirming universality through lattice-based methods.

Contribution

It identifies a subtle problem in the compactification of replica boson fields and employs a geometric lattice approach to systematically study boundary conformal field theory.

Findings

Boundary conformal field theory results match alternative calculations

Confirmed universality of entanglement entropy in quantum Lifshitz critical points

Resolved issues related to compactification of multicomponent bosons

Abstract

I discuss the von Neumann entanglement entropy in two-dimensional quantum Lifshitz criical point, namely in Rokhsar-Kivelson type critical wavefunctions. I follow the approach proposed by B. Hsu et al. [Phys. Rev. B 79, 115421 (2009)], but point out a subtle problem concerning compactification of replica boson fields: although one can define a set of new boson fields by linear combinations of the original fields, the new fields are not compactified independently. In order to systematically study boundary conformal field theory of multicomponent free bosons, I employ a geometric formulation based on compactification lattices. The result from the boundary conformal field theory agrees exactly with alternative calculations by J.-M. Stephan et al. [Phys. Rev. B 80, 184421 (2009)], confirming its universality as argued originally by B. Hsu et al.