Entanglement Entropy and Twist Fields

Abstract

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the analyzed subsystem consists of a single interval, they disagree whenever the subsystem is composed of more than one connected part. The reasons of this disagreement are explained.

25 pages, 10 figures v2: section 2.1 improved; matches published version

References in corpus (4)

• Entanglement as a Probe of Confinement
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
• Entanglement entropy in d+1 SU(N) gauge theory

Cited by in corpus (6)

• Remarks on the entanglement entropy for disconnected regions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement Entropy in the O(N) model
• Universal entanglement entropy in 2D conformal quantum critical points
• Simulating Magnetohydrodynamical Flow with Constrained Transport and Adaptive Mesh Refinement; Algorithms & Tests of the AstroBEAR Code
• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution