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 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.
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ArXiv ePrint: 1805.10651
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Wong, G. Gluing together modular flows with free fermions. J. High Energ. Phys. 2019, 45 (2019). https://doi.org/10.1007/JHEP04(2019)045
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DOI: https://doi.org/10.1007/JHEP04(2019)045