Exact solution of an integrable $J_1-J_2$ spin chain model

TL;DR

This paper constructs and proves the integrability of a Heisenberg spin chain model with complex interactions, analyzing its ground state and excitations, revealing a novel triple arched spectrum structure.

Contribution

It introduces a new integrable $J_1-J_2$ spin chain model with Dzyaloshinski-Moriya interaction and provides a general method for constructing similar models.

Findings

Ground state and elementary excitations characterized

Spinon excitation spectrum exhibits a triple arched structure

Method applicable to other models with next-nearest-neighbour couplings

Abstract

An integrable Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and Dzyaloshinski-Moriya interacton is constructed. The integrability of the model is proven. Based on the Bethe Ansatz solutions, the ground state and the elementary excitations are studied. It is shown that the spinon excitation spectrum of the present system possesses a novel triple arched structure. The method provided in this paper is general to construct new integrable models with next-nearest-neighbour couplings.