Eur. Phys. J. B 66, 361-368 (2008)
https://doi.org/10.1140/epjb/e2008-00432-2

Exact ground state of a spin ladder with a quantum phase transition

¹ Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30059 Kraków, Poland
² Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany

Corresponding author: ^a a.m.oles@fkf.mpg.de

Received: 1 August 2008
Revised: 28 October 2008
Published online: 4 December 2008

Abstract

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.