Integrability and duality in spin chains

TL;DR

This paper introduces a new family of integrable spin chain models with duality symmetry, applying it to a superconductivity model that exhibits a topological phase transition linked to the duality.

Contribution

It constructs a two-parametric integrable model with duality symmetry and applies it to develop a novel $s$-$d$ wave superconducting chain with topological properties.

Findings

Discovery of a duality symmetry connecting different non-interacting modes.

Identification of a topological phase transition in the $s$-$d$ wave Richardson-Gaudin-Kitaev chain.

The occupancy of a non-interacting mode acts as a topological order parameter.

Abstract

We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the $s$-$d$ wave Richardson-Gaudin-Kitaev interacting chain, interpolating $s$- and $d$- wave superconductivity. The phase diagram of this model has a topological phase transition that can be connected to the duality, where the occupancy of the non-interacting mode serves as a topological order parameter.