Dual -1 Hahn polynomials and perfect state transfer

TL;DR

This paper characterizes all $XX$ spin chains with perfect state transfer linked to dual -1 Hahn polynomials, identifying a known model for odd N and introducing a new system for even N.

Contribution

It provides a complete classification of $XX$ spin chains with PST associated with dual -1 Hahn polynomials, including a novel system for even N.

Findings

Recovered a known PST model for odd N

Discovered a new PST system for even N

Established connection between spin chains and dual -1 Hahn polynomials

Abstract

We find all the $XX$ spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials $R_n(x; \alpha,\beta,N)$. For $N$ odd we recover a model that had already been identified while for $N$ even, we obtain a new system exhibiting PST.