Building imaginary-time thermal field theory with artificial neural networks

TL;DR

This paper presents a novel neural network-based method to estimate effective actions in thermal quantum field theories, enabling temperature interpolation and aiding phase diagram analysis.

Contribution

Introduces a neural network approach using CANs to estimate actions in thermal field theories, allowing temperature interpolation from limited data.

Findings

Accurately constructs effective actions at specific temperatures.

Successfully estimates actions at intermediate temperatures.

Facilitates detailed phase diagram exploration.

Abstract

In this study, we introduce a novel approach in quantum field theories to estimate the action using the artificial neural networks (ANNs). The estimation is achieved by learning on system configurations governed by the Boltzmann factor, $e^{-S}$ at different temperatures within the imaginary time formalism of thermal field theory. We focus on 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method. The continuous-mixture autoregressive networks (CANs) enable the construction of accurate effective actions with tractable probability density estimation. Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles. This capability is especially valuable for the detailed exploration of phase diagrams.