Path optimization in 0+1 dimensional QCD at finite density

Akira Ohnishi; Kouji Kashiwa; Yuto Mori

Path optimization in 0+1 dimensional QCD at finite density

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arxiv 1904.11140 v1 pith:VVMQRLA5 submitted 2019-04-25 hep-lat

Yuto Mori , Kouji Kashiwa , Akira Ohnishi This is my paper · ORCID

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keywords pathoptimizationdimensionalfinitegaugeintegrallinkmethod

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abstract

We investigate the sign problem in 0+1 dimensional QCD at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented by a feedforward neural network. The integral path is then optimized to weaken the sign problem. The average phase factor is enhanced to be greater than 0.99 on the optimized path. Results with and without diagonalized gauge fixing are compared and proven to be consistent. This is the first step of applying the path optimization method to gauge theories.

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Path optimization method for the sign problem caused by fermion determinant
hep-lat 2025-02 conditional novelty 5.0 of 10

Path optimization with machine learning reproduces analytic results in the 1D lattice Thirring model, and dropping the Jacobian from the learning step still works.

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