# $su(2)$ symmetry of XX spin chains

## TL;DR

This paper demonstrates that by adjusting a uniform transverse magnetic field, inhomogeneous open XX spin chains exhibit a two-fold degeneracy and an exact $su(2)$ symmetry with nonlocal generators, linked to discrete orthogonal polynomials.

## Contribution

It reveals the presence of an exact $su(2)$ symmetry in inhomogeneous XX spin chains through magnetic field adjustment, with explicit generator computation.

## Key findings

- Two-fold degeneracy in the spectrum
- Existence of an exact $su(2)$ symmetry
- Generators depend on discrete orthogonal polynomial coefficients

## Abstract

We show that, after suitably adjusting a uniform transverse magnetic field, the generic inhomogeneous open XX spin chain has a two-fold degeneracy, and an exact $su(2)$ symmetry whose "inhomogeneous" nonlocal generators depend on coefficients that can be explicitly computed for models associated with discrete orthogonal polynomials.