Phase diagram of the two-dimensional O(3) model from dual lattice simulations

TL;DR

This paper uses dual lattice simulations to explore the phase diagram of the two-dimensional O(3) model at nonzero chemical potential, revealing a quantum phase transition and universal behaviors, and demonstrating the dual approach solves the sign problem.

Contribution

It introduces a dual lattice simulation method for the O(3) model at finite chemical potential, enabling study of its phase diagram and critical properties.

Findings

Demonstrates dual representation solves the sign problem.

Identifies a quantum phase transition at zero temperature when chemical potential equals particle mass.

Measures spin stiffness indicating a dynamical critical exponent z=2.

Abstract

We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a crossover at nonzero temperature, while at zero temperature it undergoes a quantum phase transition when mu reaches the particle mass (generated dynamically similar to QCD). The density follows a square root behavior universal for repulsive bosons in one spatial dimension. We have also measured the spin stiffness, known to be sensitive to the spatial correlation length, using different scaling trajectories to zero temperature and infinite size. It points to a dynamical critical exponent z=2. Comparisons to thermodynamic Bethe ansaetze are shown as well.