Entanglement of inhomogeneous free fermions on hyperplane lattices
- URL: http://arxiv.org/abs/2206.06509v3
- Date: Fri, 2 Jun 2023 12:08:06 GMT
- Title: Entanglement of inhomogeneous free fermions on hyperplane lattices
- Authors: Pierre-Antoine Bernard, Nicolas Cramp\'e, Rafael I. Nepomechie, Gilles
Parez, Lo\"ic Poulain d'Andecy, Luc Vinet
- Abstract summary: We introduce an ingeneous model of free fermions on a $(D-1)$-dimensional lattice with $D(D-1)/2$ continuous parameters.
We compute the entanglement entropy numerically for $D=2,3,4$, for a wide range of parameters.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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