Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model**Supported by the Natural Science Foundation for Colleges and Universities of Jiangsu Province under Grant No 16KJB140008, the National Natural Science Foundation of China under Grant Nos 11447204 and 11647164, the Natural Science Foundation of Jiangsu Province under Grant No BK20151079, and the Scientific

Abstract

To validate the ability of full configuration interaction quantum Monte Carlo (FCIQMC) for studying the 2D Hubbard model near half-filling regime, the ground state energies of a 4 × 4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization (i.e., the exact values for a given basis set) when the population of psi particles (psips) is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.