On the spin-liquid phase of one dimensional spin-1 bosons

TL;DR

This paper analyzes a one-dimensional model of spin-1 bosons with specific interactions, revealing a spin-liquid phase characterized by spin-charge separation, integrability at certain ratios, and superfluid behavior of singlet pairs.

Contribution

It derives the low energy effective field theory for the model, combining a Tomonaga-Luttinger and O(3) nonlinear sigma model, and confirms it through exact solutions at integrable points.

Findings

The system exhibits a superfluid phase of singlet boson pairs.

The low energy theory shows spin-charge separation.

Exact solutions validate the effective field theory at special ratios.

Abstract

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.