Jordan-Wigner approach to the frustrated spin one-half XXZ chain

TL;DR

This paper uses the Jordan-Wigner transformation to analyze the ground state and phase transitions of the frustrated spin-1/2 XXZ chain, comparing mean-field results with exact methods to understand its phase diagram.

Contribution

It applies a mean-field approach via Jordan-Wigner transformation to the frustrated XXZ chain and compares results with exact diagonalization, revealing insights into the phase diagram.

Findings

Good agreement with exact diagonalization near the Majumdar-Ghosh limit

Incommensurate ground states are absent for large J2 in self-consistent analysis

Ground state energy and structure factor are effectively characterized

Abstract

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the $J_1-J_2$ $XXZ$ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large $J_2$ in a fully self-consistent mean-field analysis.