MAGNETIC PROPERTIES OF HUBBARD MODEL CLASSIC.

In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.

Jul 19, 20120 citations

Magnetic and thermodynamical properties of the simple-cubic Hubbard model

Y. Kakehashi, Hideo Hasegawa

Magnetic and thermodynamical properties of the half-filled Hubbard model on the simple-cubic lattice have been investigated by using the two analytical theories for band magnetism: the single-site spin fluctuation (SSF) theory proposed independently by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) developed by Kakehashi and Fulde. We have calculated, as a function of the temperature T and the electron-electron interaction U, the sublattice magnetization, amplitude of local moments, susceptibilities, energy, and entropy, from which the U-T phase diagram is obtained. Our ground-state results, particularly of the VA, are in good agreement with those obtained in the variational Monte Carlo calculations performed by Yokoyama and Shiba. Our finite-temperature calculations are compared with those in the recent Monte Carlo (MC) simulations made by Hirsch. It is shown that, as far as local quantities such as the amplitude of local moments and the Curie constants are concerned, our results are consistent with the MC results. It is realized, however, that the antiferromagnetic correlation is much overestimated in a small 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 cluster in Hirsch's MC simulation, yielding N\'eel temperatures, ${T}_{N}$ , about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.Magnetic and thermodynamical properties of the half-filled Hubbard model on the simple-cubic lattice have been investigated by using the two analytical theories for band magnetism: the single-site spin fluctuation (SSF) theory proposed independently by Hubbard and Hasegawa and the Gutzwiller-type variational approach (VA) developed by Kakehashi and Fulde. We have calculated, as a function of the temperature T and the electron-electron interaction U, the sublattice magnetization, amplitude of local moments, susceptibilities, energy, and entropy, from which the U-T phase diagram is obtained. Our ground-state results, particularly of the VA, are in good agreement with those obtained in the variational Monte Carlo calculations performed by Yokoyama and Shiba. Our finite-temperature calculations are compared with those in the recent Monte Carlo (MC) simulations made by Hirsch. It is shown that, as far as local quantities such as the amplitude of local moments and the Curie constants are concerned, our results are consistent with the MC results. It is realized, however, that the antiferromagnetic correlation is much overestimated in a small 4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4 cluster in Hirsch's MC simulation, yielding N\'eel temperatures, ${T}_{N}$, about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.

Physical review. B, Condensed matterMay 1, 198831 citations

Magnetism in the two-dimensional Hubbard model (abstract)

J. E. Hirsch, Hsueh‐Ju Lin

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 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.

Journal of Applied PhysicsApr 15, 19850 citations

Hubbard model for a cubic cluster

J. Callaway, D. P. Chen, Yi Zhang

The ground-state and thermodynamic properties of a simple Hubbard Hamiltonian are studied for an eight-site cubic cluster as functions of the number of electrons and the strength of the electron interaction. The ground-state energy and spin are determined, and the excitation spectrum is computed. Thermodynamic properties including the specific heat, the magnetic susceptibility, and spin correlation functions are calculated. Computations are performed both by explicit diagonalization of the Hamiltonian and by Monte Carlo simulation.The ground-state and thermodynamic properties of a simple Hubbard Hamiltonian are studied for an eight-site cubic cluster as functions of the number of electrons and the strength of the electron interaction. The ground-state energy and spin are determined, and the excitation spectrum is computed. Thermodynamic properties including the specific heat, the magnetic susceptibility, and spin correlation functions are calculated. Computations are performed both by explicit diagonalization of the Hamiltonian and by Monte Carlo simulation.

Physical review. B, Condensed matterAug 1, 198730 citations

EXACT GROUND-STATE PROPERTIES OF ONE-DIMENSIONAL HUBBARD MODEL IN THE PRESENCE OF MAGNETIC FIELD

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang

The exact phase diagram and the ground-state properties of the one-dimensional Hubbard model with arbitrary on-site interaction of electrons are calculated over a wide range of magnetic field and electron concentrations by means of the Bethe-ansatz formalism. The ground-state properties, including the total energy, the average spin (magnetization) and spin (magnetic) susceptibility are investigated for both signs of the interaction strength U/t. The critical behavior near the onset of magnetization and magnetic saturation are also analyzed. At the onset of magnetization and near the magnetic saturation the spin susceptibility χ diverges at all U/t for half-filling case n=1, whereas for n≠1 it is always finite. The reverse susceptibility χ-1(U) exhibits anomalous hump, which increases with h or n, and shows discontinuity as U/t→±0 at infinitesimal h→0. The analytical results for the ground-state properties in strong and weak interaction limits are in full agreement with our numerical calculations.The exact phase diagram and the ground-state properties of the one-dimensional Hubbard model with arbitrary on-site interaction of electrons are calculated over a wide range of magnetic field and electron concentrations by means of the Bethe-ansatz formalism. The ground-state properties, including the total energy, the average spin (magnetization) and spin (magnetic) susceptibility are investigated for both signs of the interaction strength U/t. The critical behavior near the onset of magnetization and magnetic saturation are also analyzed. At the onset of magnetization and near the magnetic saturation the spin susceptibility χ diverges at all U/t for half-filling case n=1, whereas for n≠1 it is always finite. The reverse susceptibility χ-1(U) exhibits anomalous hump, which increases with h or n, and shows discontinuity as U/t→±0 at infinitesimal h→0. The analytical results for the ground-state properties in strong and weak interaction limits are in full agreement with our numerical calculations.

International Journal of Modern Physics BDec 20, 19990 citations

Ising expansion for the Hubbard model

Zhu-Pei Shi, Rajiv R. P. Singh

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.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.

arXiv:cond-mat/9507096Physical review. B, Condensed matterOct 1, 19958 citations

{T}_{N}

, about 70% higher than those in the mean-field-type theories of the SSF and VA approaches.