Entanglement of inhomogeneous free fermions on hyperplane lattices

TL;DR

This paper introduces an exactly solvable inhomogeneous free fermion model on hyperplane lattices, revealing complex entanglement behaviors including oscillations and area law violations across different dimensions.

Contribution

It presents a new exactly solvable inhomogeneous free fermion model with multidimensional Krawtchouk polynomial eigenfunctions and analyzes its entanglement properties.

Findings

Eigenfunctions are multidimensional Krawtchouk polynomials.

Oscillations in entanglement entropy for D=2.

Logarithmic area law violations for D>2.

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.