Simulation of Scalar Field Theories with Complex Actions

TL;DR

This paper introduces a local, straightforward simulation method for scalar field theories with complex actions, effectively addressing the sign problem in models with PT symmetry, and reveals rich behaviors like damped oscillations and pattern formation.

Contribution

The authors develop a novel, local simulation approach for scalar field theories with complex actions that reduces the sign problem to a manageable form and applies to models with PT symmetry.

Findings

Sign problem reduced to a sign problem for PT-symmetric models

Complete elimination of the sign problem in a large subclass of models

Observation of damped oscillations and pattern formation in simulations

Abstract

We develop a method for the simulation of scalar field theories with complex actions which is local, simple to implement and can be used in any number of space-time dimensions. For model systems satisfying the $\mathcal{PT}$ symmetry condition $L^{*}(\phi)=L(-\phi)$, the complex weight problem is reduced to a sign problem. The sign problem is eliminated completely for a large subclass of these models; this class includes models within the $i\phi^{3}$ universality class, and also models with nonzero chemical potential. Simulations of models from this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Modulated phases occur in some models, exhibiting striping and other pattern-forming behaviors. These field theory models are connected to complex systems where pattern formation occurs because of competition between interactions at two different length scales.