Entanglement Spectrum of Chiral Fermions on the Torus

Abstract

We determine the modular Hamiltonian of chiral fermions on the torus, for an arbitrary set of disjoint intervals at generic temperature. We find that, in addition to a local Unruh-like term, each point is nonlocally coupled to an infinite but discrete set of other points, even for a single interval. These accumulate near the boundaries of the intervals, where the coupling becomes increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points "condenses" within the interval at low temperatures, yielding continuous nonlocality.