# Improving efficiency of the path optimization method for a gauge theory

@article{Namekawa2022ImprovingEO,
title={Improving efficiency of the path optimization method for a gauge theory},
author={Yusuke Namekawa and Kouji Kashiwa and Hidefumi Matsuda and Akira Ohnishi and Hayato Takase},
journal={Physical Review D},
year={2022}
}
• Published 11 October 2022
• Computer Science
• Physical Review D
We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The $2$-dimensional $\text{U}(1)$ gauge theory with the complex gauge coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network…

## References

SHOWING 1-10 OF 22 REFERENCES

• Physics
Progress of Theoretical and Experimental Physics
• 2019
We investigate the sign problem in $0+1$D quantum chromodynamics at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the
• Computer Science
• 2018
The feedforward neural network is introduced to attack the sign problem via the path optimization method and the average phase factor is significantly enhanced after the optimization and then the hybrid Monte Carlo method can be safely performed.
• Physics, Computer Science
Progress of Theoretical and Experimental Physics
• 2022
This work proposes a method to represent the path integral over gauge fields as a tensor network and applies this method to three-dimensional pure SU(2) gauge theory, finding the result for the free energy agrees with the analytical results in weak and strong coupling regimes.
• Computer Science
• 2017
The parallel tempering method is implemented by taking the flow time of the anti-holomorphic gradient flow as an auxiliary variable for the highly multi-modal distribution and it is shown that this algorithm does work and correctly reproduces the analytic results for large flow times such as T=2.
• Mathematics
Progress of Theoretical and Experimental Physics
• 2021
We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost
• Computer Science
• 2020
A novel Hybrid Monte Carlo algorithm is proposed, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow, and solves the sign and multimodal problems simultaneously as the original TLTM does.
• Physics
• 1992
We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free-energy landscape (i.e., many coexisting states) at finite nonzero temperature.