An efficient quantum Monte Carlo algorithm for softcore boson systems

G. G. Batrouni, H. Mabilat

Jurij Šmakov, Kenji Harada, Naoki Kawashima

An efficient quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. It is demonstrated how this limit may be taken explicitly in the algorithm, eliminating the systematic errors. The efficiency of the algorithm is examined for the noninteracting lattice boson model and compared with the stochastic series expansion method with the heat-bath-type scattering probability of the random walker.

John A. W. Harkless, William A. Lester

Stefan Weßel, Fabien Alet, Simon Trebst +3 more

We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice.We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength.A finite critical value for entering the Tonks-Girardeau regime does not exist.Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.

Siyao Yang, Zhenning Cai, Jianfeng Lu

Abstract We present two fast algorithms which apply inclusion–exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work [2018 Inclusion–exclusion principle for many-body diagrammatics Phys. Rev. B 98 115152] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theoretical results and to compare the efficiency of the methods.

E. Slootman, Jacopo Cocomello, Saverio Moroni +2 more