Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids

TL;DR

This paper explores how entanglement entropy scales at 2D quantum Lifshitz critical points and in topological fluids, extending known 1D results to more complex 2D quantum systems and phases.

Contribution

It extends the understanding of entanglement entropy scaling from 1D conformal critical points to 2D quantum Lifshitz and topological phases, including applications to quantum dimer and fractional quantum Hall states.

Findings

Entanglement entropy exhibits specific scaling behaviors at 2D quantum Lifshitz points.

Topological phases show distinct entanglement properties compared to critical points.

Applications to quantum dimer models and fractional quantum Hall states demonstrate these concepts.

Abstract

The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have an entanglement entropy that diverges logarithmically in the subsystem size, with a universal coefficient that is is related to the central charge of the associated conformal field theory. Here I will discuss recent extensions of these ideas to a class of quantum critical points with dynamic critical exponent $z=2$ in two space dimensions and to 2D systems in a topological phase. The application of these ideas to quantum dimer models and fractional quantum Hall states will be discussed.