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

## Abstract

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.

- Authors:

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

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)

- OSTI Identifier:
- 1565609

- Grant/Contract Number:
- [ACI-1053575]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- [ Journal Volume: 96; Journal Issue: 7]; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics

### Citation Formats

```
Qin, Mingpu, Shi, Hao, and Zhang, Shiwei. Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model. United States: N. p., 2017.
Web. doi:10.1103/physrevb.96.075156.
```

```
Qin, Mingpu, Shi, Hao, & Zhang, Shiwei. Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model. United States. doi:10.1103/physrevb.96.075156.
```

```
Qin, Mingpu, Shi, Hao, and Zhang, Shiwei. Fri .
"Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model". United States. doi:10.1103/physrevb.96.075156. https://www.osti.gov/servlets/purl/1565609.
```

```
@article{osti_1565609,
```

title = {Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model},

author = {Qin, Mingpu and Shi, Hao and Zhang, Shiwei},

abstractNote = {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.},

doi = {10.1103/physrevb.96.075156},

journal = {Physical Review B},

number = [7],

volume = [96],

place = {United States},

year = {2017},

month = {8}

}

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