# Perfect State Transfer in a Spin Chain without Mirror Symmetry

## TL;DR

This paper presents an analytical asymmetric $XX$ spin chain model that enables perfect state transfer between specific sites without mirror symmetry, revealing unique transport and revival properties linked to dual -1 Hahn polynomials.

## Contribution

It introduces a novel $XX$ spin chain with asymmetrical transfer capabilities and connects its properties to dual -1 Hahn polynomial recurrence coefficients.

## Key findings

- PST occurs between even sites, not end-to-end.
- States at odd sites experience fractional revival.
- Perfect return occurs at double the PST/FR time.

## Abstract

We introduce an analytical $XX$ spin chain with asymmetrical transport properties. It has an even number $N+1$ of sites labeled by $n=0,\cdots N$. It does not exhibit perfect state transfer (PST) from end-to-end but rather from the first site to the next to last one. In fact, PST of one-excitation states takes place between the even sites: $n\leftrightarrow N-n-1$, $n=0,2,\cdots, N-1$; while states localized at a single odd site undergo fractional revival (FR) over odd sites only. Perfect return is witnessed at double the PST/FR time. The couplings and local magnetic fields are related to the recurrence coefficients of the dual -1 Hahn polynomials.