Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Qin, Mingpu; Shi, Hao; Zhang, Shiwei

doi:10.1103/physrevb.96.075156

Title: Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Journal Article · Fri Aug 25 00:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.96.075156· OSTI ID:1565609

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

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

Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin-correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half filling, we employ the constrained path AFQMC approach to eliminate the exponential computational scaling from the sign problem. The constraint employs unrestricted Hartree-Fock trial wave functions with an effective interaction strength U, which is optimized self-consistently within AFQMC. Large supercells are studied, with twist averaged boundary conditions as needed, to reach the thermodynamic limit. We find that the nearest-neighbor spin correlation always increases with the interaction strength U , contrary to the finite-temperature behavior where a maximum is reached at a finite U value. We also observe a change of sign in the next-nearest-neighbor spin correlation with increasing density, which is a consequence of the buildup of the long-range antiferromagnetic correlation. Finally, we expect the results presented in this paper to serve as a benchmark as lower temperatures are reached in ultracold atom experiments.

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

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

Grant/Contract Number:: ACI-1053575

OSTI ID:: 1565609

Journal Information:: Physical Review B, Vol. 96, Issue 7; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 6 works

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