Suwa, Hidemaro
Title: Markov Chain Monte Carlo without Detailed Balance and Bounce-free Worm Algorithm
Author: Hidemaro Suwa
Affiliation: Department of Applied Physics, the University of Tokyo, Japan
Abstract:
In the Markov chain Monte Carlo method, the detailed balance is usually imposed as a sufficient condition for the balance condition. If the Markov sequence goes beyond the detailed balance, however, rejection rates can get minimized. Although it has been considered to be difficult to generally construct a transition matrix beyond the detailed balance, we have invented a new Monte Carlo algorithm that surely makes it possible with minimized rejection rates. As a benchmark, we have confirmed that our algorithm significantly boosts up the relaxation speed in 4-state Potts model to nearly 7 times more than the heat bath algorithm and 30 times more than the Metropolis algorithm. In the same manner, we have also developed a bounce-free worm algorithm in the quantum Monte Carlo method. In one dimensional Heisenberg model with magnetic field, it is confirmed that the relaxation by the bounce-free worms gets about 50 times faster than by the conventional method called the generalized directed-loop.
Author: Hidemaro Suwa
Affiliation: Department of Applied Physics, the University of Tokyo, Japan
Abstract:
In the Markov chain Monte Carlo method, the detailed balance is usually imposed as a sufficient condition for the balance condition. If the Markov sequence goes beyond the detailed balance, however, rejection rates can get minimized. Although it has been considered to be difficult to generally construct a transition matrix beyond the detailed balance, we have invented a new Monte Carlo algorithm that surely makes it possible with minimized rejection rates. As a benchmark, we have confirmed that our algorithm significantly boosts up the relaxation speed in 4-state Potts model to nearly 7 times more than the heat bath algorithm and 30 times more than the Metropolis algorithm. In the same manner, we have also developed a bounce-free worm algorithm in the quantum Monte Carlo method. In one dimensional Heisenberg model with magnetic field, it is confirmed that the relaxation by the bounce-free worms gets about 50 times faster than by the conventional method called the generalized directed-loop.