Gluing together Modular flows with free fermions

Abstract

We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing together the single interval modular flows. Using this relation, we obtain an exact expression for the multi-interval modular Hamiltonian and entanglement entropy in agreement with existing results. An essential ingredient in our derivation is the introduction of the \emp{modular action}. This determines the non-local field theory describing the free fermion reduced density matrix, and makes manifest it's non-local conformal symmetry and $U(1)$ Kacs-Moody symmetry.

arXiv commentSubstantially revised, errors and typos corrected. 29 pages, 9 figures

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Cited by in corpus (8)

• On entanglement hamiltonians of an interval in massless harmonic chains
• Entanglement branes and factorization in conformal field theory
• Entanglement branes, modular flow, and extended topological quantum field theory
• Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
• Modular Hamiltonian of the scalar field in the semi infinite line: dimensional reduction for spherically symmetric regions
• Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory