Path optimization in field theories with sign problem

In order to avoid the sign problem appearing in some field theories such as finite density QCD, we have proposed the path optimization method [1-3]. In this method, the integral path in the complexified variable space is parametrized and optimized variationally to minimize the cost function representing the seriousness of the sign problem. Then the sign problem can be regarded as an optimization problem, in which various optimization techniques such as the machine learning are available.

The path optimization method have been applied to a one dimensional integral [1], finite density complex scalar field [2], and the Polyakov loop extended Nambu-Jona-Lasinio model [3]. In these cases, the average phase factor is enhanced significantly. In the presentation, we discuss the sign problem in finite density complex scalar field theory [2] and the 0+1 dimensional QCD.

 

[1] Y. Mori, K. Kashiwa, A. Ohnishi, Phys. Rev. D 96 (2017), 111501(R).

[2] Y. Mori, K. Kashiwa, A. Ohnishi, PTEP 2018 (2018), 023B04.

[3] K. Kashiwa, Y. Mori, A. Ohnishi, arXiv: 1805.08940 [hep-ph].