Eur. Phys. J. B 49, 283-287 (2006)
https://doi.org/10.1140/epjb/e2006-00077-1

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

¹ Institute for Condensed Matter Physics, 1 Svientsitskii Str., L'viv, 79011, Ukraine
² Technische Universität Braunschweig, Institut für Theoretische Physik, Mendelssohnstrasse 3, 38106 Braunschweig, Germany

Corresponding author: ^a werch@icmp.lviv.ua

Received: 16 November 2005
Revised: 6 January 2006
Published online: 10 March 2006

Abstract

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the J₁-J₂ 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 J₂ in a fully self-consistent mean-field analysis.