The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons

TL;DR

This paper uses dual lattice simulations to study the thermodynamics of the 2D O(3) model at nonzero density, revealing a quantum phase transition and confirming universal low-density behavior consistent with repulsive bosons.

Contribution

First dual lattice simulation of the O(3) model at nonzero density, providing new data on its phase transition and low-energy behavior.

Findings

Identified a quantum phase transition at zero temperature with nonzero density.

Observed a dynamical critical exponent close to 2.

Confirmed the universal square root behavior at low density.

Abstract

We discuss the thermodynamics of the O(3) nonlinear sigma model in 1+1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the lattice model we present, for the first time, nonzero density data of an asymptotically free theory with dynamical mass-gap. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. We present evidence for a corresponding dynamical critical exponent z close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe ansatz solutions of the relativistic and non-relativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density.