GQFI-WST Seminar: Erik Tonni "Modular Hamiltonians for the Dirac field in presence of a boundary"
The reduced density matrix of a spatial subsystem can be written as the exponential of the modular Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. In this talk, Erik Tonni (SISSA, INFN) considers the massless Dirac field on the half-line, imposing the most general boundary conditions that ensure the global energy conservation. This leads to two inequivalent phases where either the vector or the axial symmetry is preserved. In these two phases, he discusses the analytic expressions for the modular Hamiltonians of an interval on the half-line when the system is in its ground state, for the corresponding modular flows of the Dirac field and for the corresponding modular correlators. The method allows to obtain analytic expressions also for the modular Hamiltonians, the modular flows and the modular correlators for 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.
Full title of the talk: "Modular Hamiltonians for the massless Dirac field in the presence of a boundary or of a defect".
The Virtual Seminar Series “GQFI-Warsaw String Theory” (GQFI-WST) is a joint initiative between the strings/holography groups at the Albert Einstein Institute (AEI) in Potsdam and the University Warsaw. The calendar for upcoming GQFI-WST seminars can be found here: https://gqfi.aei.mpg.de/node/3.
This talk is primarily based on arXiv:2012.00703 [hep-th] (https://arxiv.org/abs/2012.00703) and arXiv:2012.01366 [hep-th] (https://arxiv.org/abs/2012.01366).
This talk was recorded on May 26th, 2021 at the Albert Einstein Institute in Potsdam-Golm.