Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials

TL;DR

This paper introduces a two-dimensional spin lattice model with perfect state transfer, utilizing bivariate dual-Hahn polynomials to define hopping amplitudes, and demonstrates fractional revival for specific parameters.

Contribution

It presents a novel two-dimensional spin lattice model with exact solvability based on bivariate dual-Hahn polynomials, enabling perfect state transfer and fractional revival.

Findings

Perfect state transfer achieved in the model

Fractional revival observed for specific parameters

Hopping amplitudes linked to bivariate dual-Hahn polynomials

Abstract

A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a specific choice of the parameters, perfect state transfer and fractional revival are shown to take place.