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Physics of the Solid State

Magnetic susceptibility of the two-dimensional two-sublattice Hubbard model calculated in the static-fluctuation approximation

G. I. Mironov

Published Jun 1, 2005• 2 citations
Publisher

Abstract

The transverse dynamic susceptibility of the 2D two-sublattice Hubbard model is calculated in the static-fluctuation approximation. The static magnetic susceptibility is studied as a function of various parameters of the system. The results for the special case of the one-dimensional Hubbard model are compared to the exact solution.
DOI
10.1134/1.1946865

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The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
The T = 0 spin stiffness ρ s and the transverse susceptibility χ ⊥ of the square lattice half-filled Hubbard model are calculated as a function of the Hubbard parameter ratio U / t by series expansions around the Ising limit. We find that the calculated spin stiffness, transverse susceptibility, and sublattice magnetization for the Hubbard model smoothly approach the Heisenberg values for large U / t . The results are compared for different U / t with RPA and other numerical studies. The uniform susceptibility data indicate a crossover around U / t ≈ 4 between weak-coupling (spin density wave) behavior at small U and strong-coupling (Heisenberg) behavior at large U .
We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U\ensuremath{\approxeq}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.