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.

arXiv comment6 pages, 3 figures

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Cited by in corpus (17)

• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• On entanglement hamiltonians of an interval in massless harmonic chains
• The entanglement spectrum of chiral fermions on the torus
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• Moving mirrors, Page curves and bulk entropies in AdS${}_2$
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• The entanglement and relative entropy of a chiral fermion on the torus
• Modular Hamiltonian for (holographic) excited states
• Symmetry-resolved modular correlation functions in free fermionic theories
• Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
• Modular conjugations in 2D conformal field theory and holographic bit threads
• Modular Hamiltonian for de Sitter diamonds
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Modular conjugation for multicomponent regions
• 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