Entanglement Hamiltonian for inhomogeneous free fermions

• URL: http://arxiv.org/abs/2403.14766v1
• Date: Thu, 21 Mar 2024 18:13:10 GMT
• Title: Entanglement Hamiltonian for inhomogeneous free fermions
• Authors: Riccarda Bonsignori, Viktor Eisler,
• Abstract summary: We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. It is shown that, for both models, conformal field theory predicts a Bisognano-Wichmann form for the entangement Hamiltonian of a half-infinite system.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. In particular, we consider a lattice with a linear, as well as a continuum system with a quadratic potential. It is shown that, for both models, conformal field theory predicts a Bisognano-Wichmann form for the entangement Hamiltonian of a half-infinite system. Furthermore, despite being nonrelativistic, this result is inherited by our models in the form of operators that commute exactly with the entanglement Hamiltonian. After appropriate rescaling, they also yield an excellent approximation of the entanglement spectra, which becomes asymptotically exact in the bulk of the trapped Fermi gas. For the gradient chain, however, the conformal result is recovered only after taking a proper continuum limit.

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