Two-dimensional Hubbard model: Numerical simulation study

TLDR

The mean‑field approximation of the two‑dimensional Hubbard model on a square lattice reveals peculiar band‑structure features. The study aims to examine properties of the attractive Hubbard model at half filling. We employ a simulation algorithm validated against exact 6‑site chain results and perform finite‑size scaling to analyze the zero‑coupling transition. Our simulations of the two‑dimensional Hubbard model on a square lattice with nearest‑neighbor hopping up to 8×8 sites show that the half‑filled system is an antiferromagnetic insulator with weaker long‑range order than mean‑field predictions, while doped systems remain paramagnetic and exhibit no tendency toward ferromagnetism or triplet superconductivity.

Abstract

We have studied the two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping. We first discuss the properties of the model within the mean-field approximation: Because of the form of the band structure, some peculiar features are found. We then discuss the simulation algorithm used and compare simulation results with exact results for 6-site chains to test the reliability of the approach. We present results for thermodynamic properties and correlation functions for lattices up to 8\ifmmode\times\else\texttimes\fi{}8 in spatial size. The system is found to be an antiferromagnetic insulator for all values of the coupling constant at zero temperature in the half-filled-band case, but the long-range order is much smaller than predicted by mean-field theory. We perform a finite-size-scaling analysis to determine the character of the transition at zero coupling. For non-half-filled-band cases, our results suggest that the system is always paramagnetic, in contradiction with Hartree-Fock predictions. The system does not show tendency to ferromagnetism nor triplet superconductivity in the parameter range studied. We also discuss some properties of the attractive Hubbard model in the half-filled-band case.