Entanglement and alpha entropies for a massive Dirac field in two dimensions

Details Entanglement and alpha entropies for a massive Dirac field in two dimensions Entanglement and alpha entropies for a massive Dirac field in two dimensions

2005-05-23

arxiv.org/abs/cond-mat/0505563v2

J.Stat.Mech.0507:P07007,2005

Physics

Condensed Matter

Other Condensed Matter

Clarification in section 2, one reference added. 15 pages, 3 figures

Scientific paper

10.1088/1742-5468/2005/07/P07007

We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the correlators of suitable operators in the sine-Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlev\'e V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.

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