Building imaginary-time thermal field theory with artificial neural networks*

Abstract

Abstract In this paper, we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks (ANNs). The actions are estimated by learning system configurations governed by the Boltzmann factor, , at different temperatures within the imaginary time formalism of thermal field theory. Specifically, we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method. 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 detailed exploration of phase diagrams.