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

## TL;DR

This paper constructs and solves an integrable anisotropic $J_1-J_2$ spin chain model, revealing unique excitation structures and effects of interactions, and offers a method to develop new integrable models with next-nearest-neighbour couplings.

## Contribution

It presents the exact solution of a new integrable anisotropic spin chain with complex interactions, including scalar chirality, and analyzes its ground state and excitations.

## Key findings

- Spinon excitation has a triple arched structure.
- Elementary excitations are gapless for real anisotropy parameter.
- Next-nearest-neighbour and chiral interactions increase the excitation gap.

## Abstract

An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The ground state and the elementary excitations are also studied. It is shown that the spinon excitation of the present model possesses a novel triple arched structure. The elementary excitation is gapless if the anisotropic parameter $\eta$ is real while the elementary excitation has an enhanced gap by the next-nearest-neighbour and chiral three-spin interactions if the anisotropic parameter $\eta$ is imaginary. The method of this paper provides a general way to construct new integrable models with next-nearest-neighbour interactions.