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

Qin, Mingpu; Shi, Hao; Zhang, Shiwei

doi:10.1103/physrevb.94.085103

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

Journal Article · Thu Aug 04 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.94.085103· OSTI ID:1565498

Qin, Mingpu ^[1]; Shi, Hao ^[1]; Zhang, Shiwei ^[1]

College of William and Mary, Williamsburg, VA (United States)

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 this paper 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 quasirandom sequences, which improves the convergence to the thermodynamic limit over pseudorandom 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 × 16 are also provided for benchmark purposes.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: National Science Foundation (NSF); Simons Foundation; USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0008627

OSTI ID:: 1565498

Alternate ID(s):: OSTI ID: 1282432

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 8 Vol. 94; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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