Entanglement of inhomogeneous free fermions on hyperplane lattices

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.