[Paper Review] Self-learning Monte-Carlo for non-abelian gauge theory with dynamical fermions

Yuki Nagai, Akinori Tanaka+1 more|arXiv (Cornell University)|Oct 22, 2020

High-Energy Particle Collisions Research4 citations

TL;DR

This paper introduces a self-learning Monte Carlo (SLMC) algorithm for non-abelian gauge theories with dynamical fermions in four dimensions, using a tunable effective action and Metropolis-Hastings updates to reduce autocorrelation. It demonstrates that SLMC reproduces HMC results for zero- and finite-temperature QCD simulations with four-flavor two-color QCD, including Polyakov loop and chiral condensate observables, and confirms reduced autocorrelation times.

ABSTRACT

In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm for non-abelian gauge theory with dynamical fermions in four dimensions to resolve the autocorrelation problem in lattice QCD. We perform simulations with the dynamical staggered fermions and plaquette gauge action by both in HMC and SLMC for zero and finite temperature to examine the validity of SLMC. We confirm that SLMC can reduce autocorrelation time in non-abelian gauge theory and reproduces results from HMC. For finite temperature runs, we confirm that SLMC reproduces correct results with HMC, including higher-order moments of the Polyakov loop and the chiral condensate. Besides, our finite temperature calculations indicate that four flavor QC${}_2$D with $\hat{m} = 0.5$ is likely in the crossover regime in the Colombia plot.

Motivation & Objective

• To address the critical slowing down problem in lattice QCD simulations using hybrid Monte Carlo (HMC) algorithms.
• To develop a machine learning-based configuration generation method that maintains exactness and avoids bias, unlike previous approaches.
• To extend the self-learning Monte Carlo (SLMC) algorithm to non-abelian gauge theories with dynamical fermions, previously applied only to classical spin models.
• To validate SLMC against HMC in both zero- and finite-temperature settings, including higher-order observables like Polyakov loop susceptibility and chiral condensate.
• To investigate the phase structure of four-flavor two-color QCD with heavy quark mass ($\hat{m}=0.5$) using SLMC, indicating a crossover regime.

Proposed method

• Adapts the self-learning Monte Carlo (SLMC) algorithm to non-abelian gauge theories with dynamical fermions using a tunable effective action derived from a hopping parameter expansion.
• Employs a Metropolis-Hastings test with a reversible, symplectic integrator to ensure detailed balance and exact convergence.
• Uses a heavy-quark mass expanded effective action with linear regression to approximate the fermionic determinant, enabling efficient updates.
• Applies heatbath updates with a dynamically generated action to improve acceptance rates and reduce autocorrelation.
• Performs simulations using the plaquette gauge action and staggered fermions on $8^3 \times 4$ lattices at zero and finite temperature.
• Compares SLMC results with HMC for observables including the Polyakov loop, chiral condensate, and their higher-order moments.

Experimental results

Research questions

• RQ1 Can the SLMC algorithm be successfully extended to non-abelian gauge theories with dynamical fermions while preserving exactness and avoiding bias?

Key findings

• SLMC successfully reduces autocorrelation times in non-abelian gauge theories with dynamical fermions, demonstrating improved sampling efficiency compared to HMC.