Method for simulating O(N) lattice models at finite density

TL;DR

This paper introduces a novel simulation method for O(N) lattice models at finite density that circumvents the complex probability weight problem, enabling accurate analysis of phase diagrams and correlation functions.

Contribution

The authors develop a new simulation technique for scalar field theories at finite density that avoids the sign problem, validated through simulations of U(1)=O(2) theories in 2+1 dimensions.

Findings

Successfully simulated free and interacting theories at finite density.

Mapped the phase diagram in the m^2-mu plane at weak coupling.

Analyzed properties near phase transitions at high self-couplings.

Abstract

We present a method for simulating relativistic and nonrelativistic scalar field theories at finite density, with matter transforming in the fundamental representation of the global symmetry group O(N). The method avoids the problem of complex probability weights which is present in conventional path integral Monte Carlo algorithms. To verify our approach, we simulate the free and interacting relativistic U(1)=O(2) theory in 2+1 dimensions. We compute the two-point correlation function and charge density as a function of chemical potential in the free theory. At weak phi^4 coupling and zero temperature we map the m^2-mu phase diagram and compare our numerical results with perturbative calculations. Finally, we compute properties of theT-mu phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential.