Normalizing flows for the real-time sign problem

TL;DR

This paper explores the use of normalizing flows to address the sign problem in bosonic lattice field theories with real-time dynamics, proposing a guaranteed solution once the flow is found.

Contribution

It introduces the concept that normalizing flows can solve the sign problem in bosonic theories and discusses why this approach may not extend to fermionic systems.

Findings

Normalizing flows can theoretically solve the sign problem in bosonic theories.

Existence of such flows is argued for bosonic but not fermionic theories.

The approach is specific to the Schwinger-Keldysh formalism.

Abstract

We discuss the application of normalizing flows to bosonic lattice field theories with real-time sign problems. A normalizing flow, once it is found for such a lattice field theory, is guaranteed to solve its sign problem. We argue for the existence of normalizing flows for bosonic lattice field theories in the Schwinger-Keldish formalism in a few ways. We then discuss how this existence is a specific feature of bosonic theories: such arguments break down for fermionic systems, whether at finite density or in real-time.