Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method

TL;DR

This study provides a comprehensive benchmark of the two-dimensional Hubbard model using advanced auxiliary-field quantum Monte Carlo techniques, achieving highly accurate ground state properties across various interaction strengths and densities.

Contribution

The paper introduces improved computational algorithms and boundary condition methods, enabling precise calculations of the Hubbard model's ground state properties for larger systems and different doping levels.

Findings

Numerically exact results at half-filling.

Enhanced convergence using quasi-random sequences.

Accurate thermodynamic limit estimates through finite size scaling.

Abstract

Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/t from 2 to 8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75, and 0.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasi-random sequences, which improves the convergence to the thermodynamic limit over pseudo-random and other sequences. With it and a careful finite size scaling analysis, we are able to obtain accurate values of ground state properties in the thermodynamic limit. Detailed results for finite-sized systems up to 16 \times 16 are also provided for benchmark purposes.