Rényi entropies of the massless Dirac field on the torus

Authors:
Open Access
Publisher website
Google Scholar
Abstract
We compute the Rényi entropies of the massless Dirac field on the Euclidean torus (the Lorentzian cylinder at nonzero temperature) for arbitrary spatial regions. We do it by the resolvent method, i.e., we express the entropies in terms of the resolvent of a certain operator and then use the explicit form of that resolvent, which was obtained recently. Our results are different in appearance from those already existing in the literature (obtained via the replica trick), but they agree perfectly, as we show numerically for noninteger order and analytically for integer order. We also compute the Rényi mutual information, and find that, for appropriate choices of the parameters, it is nonpositive and nonmonotonic. This behavior is expected, but it cannot be seen with the simplest known Rényi entropies in quantum field theory because they are proportional to the entanglement entropy.
Funding Information
  • Consejo Nacional de Investigaciones Científicas y Técnicas (UBACyT 20020190200162BA)
  • Agencia Nacional de Promoción Científica y Tecnológica (PICT-2018-03593)

This publication has 31 references indexed in Scilit: