Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum

TL;DR

This paper investigates the entanglement entropy of 2D conformal quantum critical points, revealing a universal logarithmic correction determined by geometry and conformal field theory parameters, extending understanding beyond 1D systems.

Contribution

It provides the first analysis of entanglement entropy for 2D conformal quantum critical points, identifying a universal logarithmic correction linked to geometry and central charge.

Findings

Universal logarithmic correction depends on geometry and central charge.

Entanglement entropy includes a nonuniversal area law term.

Results extend entanglement entropy understanding to 2D conformal critical points.

Abstract

The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ 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 entanglement that diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find the entanglement entropy for a standard class of $z=2$ quantum critical points in two spatial dimensions with scale invariant ground state wave functions: in addition to a nonuniversal ``area law'' contribution proportional to the size of the $AB$ boundary, there is generically a universal logarithmically divergent correction. This logarithmic term is completely determined by the geometry of the partition into subsystems and the central charge of the field theory that describes the equal-time correlations of the critical wavefunction.