David Logan

Abstract:

We study the collective excitation spectrum of a d = 3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder-interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.

Abstract:

A theory is developed for the T = 0 Mott-Hubbard insulating phases of the d∞ Hubbard model at 1/2·filling. including both the antiferromagnetic (AF) and paramagnetic (P) insulators. Local moments are introduced explicitly from the outset, enabling ready identification of the dominant low-energy scales for insulating spin-flip excitations. Dynamical coupling of single-particle processed to the spin-flip excitations leads to a renormalized self-consistent description of the single-particle propagators that is shown to be asymptotically exact in strong coupling. for both the AF and P phases. For the AF case, the resultant theory is applicable over the entire U-range, and is discussed in some detail. For the P phase, we consider in particular the destruction of the Mott insulator, the resultant critical behaviour of which is found to stem inherently from proper inclusion of the spin-flip excitations.

Abstract:

To understand the electronic properties - in particular the metal -insulator transition (MIT) - of cubic tungsten bronzes NaxWO3 and NaxTayW1-yO3, a microscopic model incorporating electron interactions and correlated disorder is presented and treated at the mean-field level of unrestricted Hartree-Fock. The conduction band is found to exhibit a pseudogap at the Fermi level for sufficiently large interaction strengths, in agreement with experiment. The pseudogap has a profound effect on localization properties of Fermi-level states and the position of the MIT. The lower band-edge states are found to be essentially two-dimensional, with a progressive crossover to three-dimensional character with increasing energy. An exception to this behaviour occurs in the pseudogap, where the states are virtually two-dimensional.

Abstract:

We describe a new approach to the ground state antiferromagnetic phase of the infinite-dimensional Hubbard model. The theory recovers correctly both the strong coupling Heisenberg limit at ½ filling and the t-J limit in the one-hole sector, appears applicable over a wide U range, and is readily extended to finite dimensions. © 1996 The American Physical Society.

Abstract:

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 Néel 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. © 1996 The American Physical Society.