Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition

TL;DR

This paper introduces a novel Bethe ansatz method to exactly analyze an anisotropic quantum spin chain with competing interactions and twisted boundary conditions, revealing unique elementary excitations and dispersion relations.

Contribution

A new Bethe ansatz scheme is developed for an integrable spin chain with twisted boundary conditions, providing exact solutions for ground state and excitations.

Findings

Exact ground state energy and rapidity density calculated

Three types of elementary excitations identified

Dispersion relations differ from periodic boundary condition case

Abstract

A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where the boundary condition is the twisted one. The eigenvalue of the transfer matrix is characterized by its zero roots instead of the traditional Bethe roots. Based on the exact solution, the conserved momentum and charge operators of this U(1)-symmetry broken system are obtained. The ground state energy and density of rapidities are calculated. It is found that there exist three kinds of elementary excitations and the corresponding dispersion relations are obtained, which gives a different picture from that with periodic boundary condition.