Modular Hamiltonian of a chiral fermion on the torus

Abstract

We consider a chiral fermion at non-zero temperature on a circle (i.e., on a torus in the Euclidean formalism) and compute the modular Hamiltonian corresponding to a subregion of the circle. We do this by a very simple procedure based on the method of images, which is presumably generalizable to other situations. Our result is non-local even for a single interval, and even for Neveu-Schwarz boundary conditions. To the best of our knowledge, there are no previous examples of a modular Hamiltonian with this behavior.

6 pages, 3 figures

References in corpus (4)

• Towards a derivation of holographic entanglement entropy
• Relative entropy and the Bekenstein bound
• Entanglement hamiltonians in two-dimensional conformal field theory
• Universality of Gravity from Entanglement

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• Rényi entropies of the massless Dirac field on the torus
• Modular Hamiltonian for fermions of small mass
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density