Worldvolume tempered Lefschetz thimble method and its error estimation

Abstract

The worldvolume tempered Lefschetz thimble method (WV-TLTM) is an algorithm towards solving the sign problem, where hybrid Monte Carlo updates are performed on a continuous accumulation of flowed surfaces foliated by the anti-holomorphic gradient flow (the worldvolume of integration surface). Sharing the advantage with the original tempered Lefschetz thimble method (TLTM) that the sign problem is resolved without introducing the ergodicity problem, the new algorithm is expected to significantly reduce the computational cost, because it eliminates the need to compute the Jacobian of the flow in generating a configuration. We demonstrate the effectiveness of the WV-TLTM with its successful application to the Stephanov model (a chiral random matrix model), for which the complex Langevin method is known to suffer from a serious wrong convergence problem. We also discuss the statistical analysis method for the WV-TLTM.