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Journal Articles Nucl.Phys.B Year : 2022

Entanglement of inhomogeneous free fermions on hyperplane lattices

Abstract

We introduce an inhomogeneous model of free fermions on a (D1)-dimensional lattice with D(D1)/2 continuous parameters that control the hopping strength between adjacent sites. We solve this model exactly, and find that the eigenfunctions are given by multidimensional generalizations of Krawtchouk polynomials. We construct a Heun operator that commutes with the chopped correlation matrix, and compute the entanglement entropy numerically for D=2,3,4, for a wide range of parameters. For D=2, we observe oscillations in the sub-leading contribution to the entanglement entropy, for which we conjecture an exact expression. For D>2, we find logarithmic violations of the area law for the entanglement entropy with nontrivial dependence on the parameters.
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Dates and versions

hal-03708505 , version 1 (11-10-2022)

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Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie, Gilles Parez, Loïc Poulain d'Andecy, et al.. Entanglement of inhomogeneous free fermions on hyperplane lattices. Nucl.Phys.B, 2022, 984, pp.115975. ⟨10.1016/j.nuclphysb.2022.115975⟩. ⟨hal-03708505⟩
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