Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

TL;DR

This paper develops a method to analyze ground-state entanglement entropy in inhomogeneous free-boson models, using orthogonal polynomials, and demonstrates its effectiveness through exact solutions and numerical validation.

Contribution

Introduces a new analytical approach for entanglement scaling in inhomogeneous free-boson systems using orthogonal polynomials.

Findings

Method accurately predicts entanglement entropy scaling.

Analytical results match numerical simulations.

Applicable to a broad class of inhomogeneous models.

Abstract

In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading term in the entanglement scaling, based on the analytic properties of the inhomogeneous potential. This method is applicable to a broad class of models with smooth spatial inhomogeneities. As a case study, we apply this approach for a family of exactly-solvable models characterized by orthogonal polynomials of the Askey scheme, finding a perfect match between the numerical and analytical results.