Rényi entropies of the massless Dirac field on the torus

Abstract

We compute the Rényi entropies of the massless Dirac field on the Euclidean torus (the Lorentzian cylinder at non-zero 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 non-integer order and analytically for integer order. We also compute the Rényi mutual information, and find that, for appropriate choices of the parameters, it is non-positive and non-monotonic. 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.

11 pages, 8 figures

References in corpus (8)

• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement Entropy at Large Central Charge
• Relative entropy and the Bekenstein bound
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• A c-theorem for the entanglement entropy
• Modular Hamiltonian of a chiral fermion on the torus
• Mutual information and the F-theorem
• Four Lectures on Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics