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Conference on Multimedia Modeling

Comparison of the magnetic properties of the Hubbard Hamiltonian in the weak correlation limit to the HFA

L. C. Bartel, H. S. Jarret

Published Jan 1, 1974• 0 citations
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Comparison of the magnetic properties of the Hubbard hamiltonian in the weak correlation limit to the HFA. [Susceptibility; density of states; spin-spin correlation]

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Helicity modulus and effective hopping in the two-dimensional Hubbard model using slave-boson methods

P J H Denteneer, M. Blaauboer

The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak and strong ferromagnetism and antiferromagnetism is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about three along both the t/U and density axes compared to the HFA. Using the spin-rotation-invariant formulation of the slave-boson method the helicity modulus is computed and for half filling is found practically to coincide with that found using variational Monte Carlo calculations with the Gutzwiller wave function. Off half filling the results can be used to compare with quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half filling.

arXiv:cond-mat/9406093•Journal of Physics Condensed Matter•Jan 2, 1995•14 citations
Resonance broadening is included along with spin‐disorder scattering to study the magnetic properties of the Hubbard Hamiltonian in the weak correlation limit. The calculated susceptibility is compared to the exchange enhanced Hartree–Fock approximation (HFA) susceptibility, and limits are set on the applicability of the HFA. For a semicircular density of states, HFA appears to be applicable for I/Δ<0.5 and a half‐filled band, but for low electron (or hole) densities the range of applicability in I/Δ decreases.
The attractive Hubbard model for normal and superconducting ground states is examined for arbitrary electron concentration by the use of the slave-boson mean-field approximation (SBMFA) technique. This approach, at a saddle-point level, is equivalent to the Gutzwiller approximation. Several superfluid characteristics of the model are shown for hypercubic lattices of all dimensions, including , and a comparison with the Bardeen-Cooper-Schrieffer Hartree-Fock approximation (BCS-HFA) calculations and exact results is made. Our results show quantitative and qualitative corrections of the SBMFA to the HFA. The improvement of the SBMFA over the HFA diminishes with increasing lattice dimensionality. We have also evaluated the energy difference between the superconducting and the normal states; this is compared with available results for the superconducting critical temperatures in various dimensions and Uemura-type plots are obtained. The results confirm and substantiate the assertion of a continuous evolution of the superfluid properties of the model from the weak-coupling (BCS-like) to the strong-coupling (composite-boson superconductivity) limit.
The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak and strong ferromagnetism and antiferromagnetism is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about three along both the t/U and density axes compared to the HFA. Using the spin-rotation-invariant formulation of the slave-boson method the helicity modulus is computed and for half filling is found practically to coincide with that found using variational Monte Carlo calculations with the Gutzwiller wave function. Off half filling the results can be used to compare with quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half filling.