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Low Temperature Physics

Paramagnetism in the Hubbard model with strong repulsion

R. O. Zaǐtsev, Yu. V. Mikhaǐlova

Published Nov 1, 1996• 0 citations
Publisher

Abstract

The spin magnetic susceptibility is determined in the self-consistent field approximation. It is shown that in the case of a square lattice as well as a triangular lattice with a negative hopping integral, the system retains its paramagnetic properties for all electron concentrations n<l. In the case of a triangular lattice with a positive hopping integral, the system goes over to the ferromagnetic state for a concentration close to 0.4.

DOI
10.1063/10.0034132

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The spin magnetic susceptibility is determined in the self-consistent field approximation. It is shown that in the case of a square lattice as well as a triangular lattice with a negative hopping integral, the system retains its paramagnetic properties for all electron concentrations n<l. In the case of a triangular lattice with a positive hopping integral, the system goes over to the ferromagnetic state for a concentration close to 0.4.
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We study the temperature-dependent spin susceptibility of a structurally disordered Hubbard model with a quasi-exponential transfer integral based on a hydrogenic 1 s wavefunction. The electronic hopping is treated perturbatively up to fourth order. The susceptibility is calculated for various atomic concentrations and electronic densities and for different strengths of on-site Coulomb repulsion. Contact is made with the measured susceptibility of lightly doped semiconductors. The possibility for ferromagnetism in the model is examined and conclusions analogous to Nagaoka's theorem and Kanamori's theory are obtained. Finally, using a generalized Kirkwood superposition approximation for the many-body distribution functions, we have investigated the influence of short-range atomic correlation on the magnetic properties.
The authors determine the ground-state phase diagram of the Hubbard model on the square lattice allowing for homogeneous spiral, antiferromagnetic, ferromagnetic and paramagnetic phases in the overall parameter range. This is obtained from a saddle-point approximation of a spin-rotation-invariant form of the slave-boson representation introduced by Kotliar and Ruckenstein (1986). In addition they determine analytically the transition point for infinite repulsive interaction strength between the Nagaoka state and the paramagnetic state on any bipartite lattice.
We present an approach to the magnetic properties of the half-filled Hubbard model, based on an approximate mapping of its low-energy transverse spin excitations on to those of an effective underlying Heisenberg model, but with effective spin interactions which are self-consistently determined and not confined solely to nearest-neighbor couplings. The mapping is exact in strong-coupling and is found to be accurate over a very wide range of interaction strengths, down to weak coupling. At zero temperature, it permits ready evaluation at finite U of the one-loop effects of zero-point spin fluctuations on, e.g., the sublattice magnetization. At finite temperatures, thermodynamic properties of the system in the thermal paramagnet are studied via a physically transparent Onsager reaction field approach, which amounts to a self-consistent treatment of paramagnetic spin correlations. This is central not only in recovering the correct dimensionality dependence of antiferromagnetic long-ranged order, but also for the d=3 case of primary interest here yields a N\'eel temperature in close agreement with known strong- and weak-coupling limits. Spin correlation functions and magnetic susceptibilities also show very good agreement with quantum Monte Carlo calculations over an appreciable temperature range in which the low-lying transverse spin excitations are thermally dominant. \textcopyright{} 1996 The American Physical Society.
We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for special filling factors and when the lattice anisotropy parameter takes some critical value, which depends on the size of the lattice strip. Near this critical point two states with marginal values of the total spin, both of which can be a ground state before or after the transition, are locally stable against a few flips of spins.