Path modification method for the sign problem
- Prof. Akira OHNISHI
- Prof. Akira OHNISHI (Yukawa Institute for Theoretical Physics, Kyoto University)
We propose a path modification method to evade the sign problem in the Monte-Carlo calculations for complex actions.
Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are currently considered to be promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points, cuts or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem.
One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points. For example, by specifying the one-dimensional integration-path as $z=t+if(t)$, where $f(t)$ is a real function of the real integration variable $t$ and is optimized to reduce the weight cancellation, we have confirmed that we can avoid the sign problem for some of the actions with which the complex Langevin method is found to fail.
In the presentation, we discuss how we can avoid the sign problem in some toy models with one field variable. We also plan to discuss the multi-variable problem, where their correlation becomes important.
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Nonzero Temperature and Density