Development and application of fundamental algorithms solving the sign problem in Monte Carlo calculations
Project Gist
Developing a versatile solution to the sign problem in Monte Carlo calculations
Keywords
Monte Carlo method, sign problem, Lefschetz thimble, tempering method, quantum chromodynamics at finite density
Background and Purpose
The sign problem in Monte Carlo calculations appears in various fields of natural science, not limited to physics, and a versatile solution has long been coveted. The “tempered Lefschetz thimble method (TLT method)” developed by us (Fukuma and Umeda) has been found to be useful in terms of both versatility and high reliability [1]. The purpose of this research project is to further improve this algorithm and apply it to various problems in physics, in order to activate those fields at one time whose progress has been stagnant due to the sign problem.
[1] M. Fukuma and N. Umeda, “Parallel tempering algorithm for integration over Lefschetz thimbles”,
PTEP 2017 (2017) 073B01.
Project Achievements
We applied the TLT method to simplified models of strongly correlated electron systems and finite density quantum chromodynamics, and showed that the TLT method gives correct results in all cases. We have also succeeded in improving the calculation algorithm of the TLT method. With these achievements, our TLT method is beginning to be recognized as one of the most powerful methods for the sign problem. The research results were published as five treatises, and were presented at a total of six international conferences (although the number declined in 2020 due to the new corona virus). We also established a network with researchers in various fields other than particle physics.
Future Prospects
In order to establish the status as an originative work from Japan, the TLT method needs to be easy to use for many researchers. In the near future, while further developing the algorithm, I would like to expand the scope of application at one time and create a large academic flow centered on solving the sign problem.
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Principal Investigator
FUKUMA Masafumi
Graduate School of Science
Prof. Fukuma received his PhD from the University of Tokyo. He has been working on theoretical high energy physics, especially on the clarification of the dynamics of quantum field theories and the construction of quantum gravity theory. He is trying to explain the fundamental laws and initial conditions of the Universe by randomness.