F. H. L. Essler 1, G. V. Shlyapnikov 2, 3, A. M. Tsvelik 4
Journal of Statistical Mechanics: Theory and Experiment (2008) 020027
We consider a model of one dimensional spin-1 bosons with repulsive density-density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin-charge separated theory of a Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density-density to spin-spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.
- 1. The Rudolf Peirls Centre for Theoretical Physics,
University of Oxford - 2. Van der Waals-Zeeman Institute,
University of Amsterdam - 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI – Paris Sud - 4. Department of Condensed Matter Physics and Material Science,
Brookhaven National Laboratory