Itinerant-Electron Magnetism in the Heisenberg Limit

TL;DR

This paper investigates the nature of itinerant-electron magnetism in the Heisenberg limit of the Hubbard model, revealing how the Kondo temperature and magnetic behavior depend on dimensionality, frustration, and temperature.

Contribution

It introduces a theoretical framework showing how itinerant-electron magnetism emerges in the Heisenberg limit, emphasizing the role of the Kondo mechanism and RVB effects.

Findings

Kondo temperature is enhanced by RVB mechanism.

Electrons behave as localized spins at high T, itinerant at low T.

Magnetic behavior varies from local-moment to itinerant-electron depending on T_N and dimensionality.

Abstract

The Hubbard model in the Heisenberg limit is studied by Kondo-lattice theory. The Kondo temperature T_K or k_BT_K, which is an energy scale of low-energy local quantum spin fluctuations, is enhanced by the resonating valence bond (RVB) mechanism, so that T_K\simeq T_MF/(2D), where T_MF is the Neel temperature in the mean-field approximation of the corresponding Heisenberg model and D is the spatial dimensionality. Electrons certainly behave as localized spins at T\gg T_K, but they are still itinerant at T\ll T_K unless an antiferromagnetic complete gap opens. When the Neel temperature T_N is so high that T_N\gg T_MF/(2D), magnetism is prototypic local-moment magnetism. When T_N is so low that T_N \ll T_MF/(2D) because of low dimensionality or frustration, magnetism is itinerant-electron magnetism of an almost spin liquid, i.e., a normal Fermi liquid or a Tomonaga-Luttinger liquid in which the spectral weight of single-particle excitations is almost vanishing. The spin susceptibility has a temperature and wave-number dependence characteristic of itinerant-electron magnetism. This type of itinerant-electron magnetism must also be possible in the Heisenberg model.