Lattice Scalar Field Theory At Complex Coupling

TL;DR

This paper explores advanced computational techniques like complex normalizing flows and contour deformations to address sign problems in lattice scalar field theories with complex couplings, enabling calculations in previously intractable regimes.

Contribution

It introduces the application of complex normalizing flows and contour deformation methods to scalar field theories with complex couplings, demonstrating their effectiveness in bypassing sign problems.

Findings

Sign problems can be bypassed using complex normalizing flows and contour deformations.

Methods extend to negative couplings via analytic continuation.

Partition function zeros relate to algorithm performance.

Abstract

Lattice scalar field theories encounter a sign problem when the coupling constant is complex. This is a close cousin of the real-time sign problems that afflict the lattice Schwinger-Keldysh formalism, and a more distant relative of the fermion sign problem that plagues calculations of QCD at finite density. We demonstrate the methods of complex normalizing flows and contour deformations on scalar fields in $0+1$ and $1+1$ dimensions, respectively. In both cases, intractable sign problems are readily bypassed. These methods extend to negative couplings, where the partition function can be defined only by analytic continuation. Finally, we examine the location of partition function zeros, and discuss their relation to the performance of these algorithms.