Off-diagonal Bethe ansatz and exact solution of a topological spin ring

TL;DR

This paper introduces a new method to solve integrable models lacking U(1) symmetry, exemplified by deriving the exact spectrum of a topological XXZ spin ring with Möbius boundary conditions, revealing its nontrivial topological excitations.

Contribution

A novel approach for constructing Bethe ansatz equations for models without U(1) symmetry, demonstrated on a topological spin ring with exact solutions.

Findings

Exact spectrum of the topological XXZ spin ring derived

Elementary excitations exhibit nontrivial topological properties

Modified T-Q relation effectively captures the model's spectrum

Abstract

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by constructing a modified T-Q relation based on the functional connection between the eigenvalues of the transfer matrix and the quantum determinant of the monodromy matrix. With the exact solution, the elementary excitations of the topological XX spin ring is discussed in detail. It is found that the excitation spectrum indeed shows a nontrivial topological nature.