Topological phases and topological entropy of two-dimensional systems with finite correlation length

by Stefanos Papanikolaou, Kumar S. Raman and Eduardo Fradkin

This nicely written paper begins with a survey of the current understanding of topological entropy. They then proceed to compute it in three new cases involving a finite correlation length, going beyond the idealized models studied in the past.

The topological entropy is a universal subleading correction of the non-universal von Neumann entropy. Levin and Wen and Kitaev and Preskil show how this subleading correction may be extracted in the limit of a small correlation length and that it is related to the "quantum dimension" of the topological phase.

The authors of the current paper demonstrate that a finite correlation length introduces corrections to this subleading term as expected from geometry effects (see last equation of section III, for example). The therefore verify explicitly that the topological entropy is universal.