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arXiv · 2206.06509

Entanglement of inhomogeneous free fermions on hyperplane lattices

Pierre-Antoine Bernard·Nicolas Crampé·Rafael I. Nepomechie·Gilles Parez·Loïc Poulain d'Andecy·Luc Vinet
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Abstract

We introduce an inhomogeneous model of free fermions on a $(D-1)$-dimensional lattice with $D(D-1)/2$ 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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Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie, Gilles Parez, Loïc Poulain d'Andecy, Luc Vinet. 2022-06-13. Entanglement of inhomogeneous free fermions on hyperplane lattices. https://doi.org/10.1016/j.nuclphysb.2022.115975

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