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

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.

16 pages, 17 figures; finite size analysis and a second version of the lattice phase diagram added, minor modifications of the text, conclusions unchanged

References in corpus (2)

• Progress towards quantum simulating the classical O(2) model
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram

Cited by in corpus (3)

• Few-body physics on a space-time lattice in the worldline approach
• Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential
• Tensor RG calculations and quantum simulations near criticality