Perfect state transfer in inhomogeneous XX model of q-Racah type

TL;DR

This paper introduces new exactly solvable inhomogeneous XX spin chain models based on q-Racah polynomials that enable perfect quantum state transfer, with explicit conditions derived from orthogonal polynomial properties.

Contribution

It presents a novel class of inhomogeneous XX models with perfect state transfer, linked to q-Racah polynomials, and provides explicit conditions for achieving this transfer.

Findings

Models exhibit perfect state transfer due to polynomial structure

Explicit conditions for parameters are derived

Analytical solutions for one-excitation sector are provided

Abstract

New exactly solvable one-dimensional XX spin chain models that exhibit perfect state transfer are defined. These models have inhomogeneous couplings and magnetic fields determined from the three-term recurrence relations satisfied by the q-Racah and para q-Racah polynomials. Due to this connection with orthogonal polynomials, the one-excitation sector can be solved analytically. This allows us to provide explicit sets of conditions on the polynomial parameters that guarantee the occurrence of perfect state transfer across these spin chains.