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Gluing together Modular flows with free fermions
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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.
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Modular Hamiltonian and entanglement entropy in the BMS free fermion theory
In the BMS free fermion model, the two-interval modular Hamiltonian has local plus bi-local terms, and the vacuum entanglement entropy for n intervals is the chiral-CFT formula with c_L=1 and c_M=0.
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