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Entanglement Hamiltonians for the massless Dirac field
Speaker: Erik Tonni (SISSA - Trieste)
The reduced density matrix of a spatial subsystem can be written as the exponential of the entanglement (modular) Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. For some particular models, states and bipartitions, this operator is local, but in general it is expected to be non-local. We study this feature for the massless Dirac field in one spatial dimension, either on the line or on the half-line. For one and two disjoint intervals on the line, we discuss the derivation of the local and bi-local terms of the entanglement Hamiltonian through the continuum limit of lattice results.
On the half-line, we consider the bipartition given by an interval in generic position. Imposing the most general boundary conditions ensuring the global energy conservation leads to two inequivalent phases where either the vector or the axial symmetry is preserved. In these two phases, we find analytic expressions for the modular Hamiltonians of an interval on the half-line when the system is in its ground state, for the the modular flows of the Dirac field and for the modular correlators. The continuum limit of lattice results is also discussed.
The method can be employed to obtain analytic expressions for the modular Hamiltonians, the modular flows and the modular correlators when the bipartition is given by two disjoint equal intervals at the same distance from a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission.
Host: Ananda Roy