# Antikink dispersions of the $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain

## TL;DR

This paper derives the antikink dispersion relations for an anisotropic $J_1$-$J_2$ sawtooth spin-1/2 Heisenberg antiferromagnetic chain, providing insights into its spin-gap, ground state energy, and thermodynamic properties.

## Contribution

It presents the first analytic dispersion relations for three antikink states and exact ground state energy at the symmetric point, advancing understanding of this frustrated quantum spin chain.

## Key findings

- Derived antikink dispersion relations for three states
- Estimated spin-gap, specific heat, and susceptibility numerically
- Identified low-temperature peak in specific heat due to frustration

## Abstract

Antikink dispersion of the asymmetric $J_1$-$J_2$ sawtooth spin-1/2 anisotropic Heisenberg antiferromagnetic chain has been derived. Value of spin-gap is obtained by estimating the minimum of dispersion relation variationally. The exact doubly-degenerate ground state energy has been derived at the symmetric point, $J_1=J_2$, for the whole anisotropic regime. Analytic form of dispersion relations of three different antikink states is obtained and their validity in the parameter space is discussed. The value of spin-gap, specific heat and susceptibility are estimated numerically by diagonalizing the Hamiltonian for chains of finite length. The inherent frustration of this antiferromagnetic model leads to the appearance of additional peak at low-temperatures in the specific heat.