Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm
arXiv:2107.06858
Abstract
We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost of the tempered Lefschetz thimble method. In the WV-HMC algorithm, the configuration space is a continuous accumulation (worldvolume) of deformed integration surfaces, and sample averages are considered for various subregions in the worldvolume. We prove that, if a sample in the worldvolume is generated as a Markov chain, then the subsample in the subregion can also be regarded as a Markov chain. This ensures the application of the standard statistical techniques to the WV-HMC algorithm. We particularly investigate the autocorrelation times for the Markov chains in various subregions, and find that there is a linear relation between the probability to be in a subregion and the autocorrelation time for the corresponding subsample. We numerically confirm this scaling law for a chiral random matrix model.
arXiv comment16 pages, 6 figures
References in corpus (15)
- On the Phase Diagram of QCD
- Random matrix model of QCD at finite density and the nature of the quenched limit
- High density QCD on a Lefschetz thimble?
- Analytic Continuation Of Chern-Simons Theory
- Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
- Adaptive stepsize and instabilities in complex Langevin dynamics
- A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
- New insights into the problem with a singular drift term in the complex Langevin method
- Toward solving the sign problem with path optimization method
- Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
- Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
- Parallel tempering algorithm for integration over Lefschetz thimbles
- Tempered transitions between thimbles
- Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling
- Implementation of the HMC algorithm on the tempered Lefschetz thimble method