Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model

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.

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

“…The FCIQMC method was originally developed for fermionic many-body problems. It has been applied to the electronic structure of molecules and solids [60][61][62] and the Hubbard model [63][64][65]. Recently, it was used to study the yrast states in a superfluid of spin- 1 2 fermions [66].…”

Slater determinant and exact eigenstates of the two-dimensional Fermi–Hubbard model

“…The two-dimensional Fermi-Hubbard model is important when attempting to understand strongly correlated electronic systems. [1][2][3][4][5] In the model, the electrons can hop from one site to its nearest neighbors and there will be an interaction between two electrons when they are on the same site. The competition between the electron hopping and the on-site electron interaction makes it hard to find exact eigenstates of the model.…”