Building imaginary-time thermal field theory with artificial neural networks

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.

8 pages, 4 figures. Accepted at Chinese Phys. C

References in corpus (23)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Instantons in QCD
• Ab-initio Determination of Light Hadron Masses
• Critical slowing down and error analysis in lattice QCD simulations
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Lattice QCD at Finite Density -- An introductory review
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Lattice QCD and heavy ion collisions: a review of recent progress
• Quantum weights of dyons and of instantons with non-trivial holonomy
• Exploring QCD matter in extreme conditions with Machine Learning
• Machine learning action parameters in lattice quantum chromodynamics
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Fourier-Flow model generating Feynman paths
• Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology
• Gradient flow exact renormalization group
• Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
• Topological objects in QCD
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Emergent Kink Statistics at Finite Temperature