Michael A. Tusch

A local moment approach to the Anderson model

A theory is developed for the single-particle spectra of the symmetric Anderson model, in which local moments are introduced explicitly from the outset. Dynamical coupling of single-particle processes to low-energy spin-flip excitations leads, within the framework of a two-self-energy description, to a theory in which both low- and high-energy spectral features are simultaneously captured, while correctly preserving Fermi liquid behaviour at low energies. The atomic limit, non-interacting limit and strong-coupling behaviour of the spectrum are each recovered. For strong coupling in particular, both the exponential asymptotics of the Kondo resonance and concomitant many-body broadening of the Hubbard satellite bands are shown to arise naturally within the present approach.

ONSAGER REACTION FIELD THEORY OF THE HEISENBERG MODEL

We discuss a simple Onsager reaction field treatment of the Heisenberg model. For d = 2 in particular, this predicts correctly the absence of long-range order for any T > 0, produces an exponentially divergent correlation length as T → 0, and gives good quantitative agreement over a wide temperature range with both Monte Carlo and (where appropriate) high-temperature series expansions.

Insulating phases of the Hubbard model

A theory is developed for the T = 0 Mott - Hubbard insulating phases of the Hubbard model at -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 processes 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.A theory is developed for the T=0 Mott-Hubbard insulating phases of the infinite-dimensional Hubbard model at half-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 processes 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.

The metal-insulator transition in disordered tungsten bronzes. Results of an Anderson-Mott-Hubbard model

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 i 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.

Magnetic response of local moments in disordered metals

We study the magnetic response properties of both site and spatially disordered Anderson-Hubbard models via a random-phase-type approximation for collective excitations about stable, inhomogeneous mean-field ground states. For the site-disordered model, zero-temperature transitions between paramagnetic, disordered antiferromagnetic and spin-glass-like ground states are examined. Within broken symmetry phases, a microscopic picture of the response of the inhomogeneous distribution of local magnetic moments to an external field is obtained, and the role of disorder in leading to a strong site differential enhancement in local susceptibilities is highlighted.

Spin interactions in an Anderson-Hubbard model

We study the magnetic properties of a site-disordered Anderson-Hubbard model at half-filling on a simple cubic lattice, via a mapping of its low-frequency transverse spin excitations onto those of an effective underlying Heisenberg model with self-consistently determined exchange couplings. Exact in the strong-coupling limit, the mapping remains accurate over the dominant region of the phase plane where the ground state is a disordered antiferromagnet. The effect of disorder and interaction strength on the resultant exchange couplings is examined in detail, and rationalized microscopically. Frustration is found to occur, even within the antiferromagnetic phase, although the ground state is shown to be stable with respect to zero-point quantum spin fluctuations. To probe finite-temperature magnetic properties, an Onsager reaction-field approach to the effective Heisenberg model in the paramagnetic phase is employed. We focus on the effect of disorder on the Neel temperature and the nature of the thermal transition to the ordered phase.

Interplay between disorder and electron interactions: mean-field phase diagram of an Anderson-Hubbard model

Abstract To obtain a broad understanding of the combined effects of disorder and electron interactions, the phase diagram of a half-filled Gaussian site-disordered Anderson-Hubbard model is assessed numerically on a simple cubic lattice, at the unrestricted Hartree-Fock mean field level. Metallic/insulating and magnetic phases are considered. Paramagnetic, disordered antiferromagnetic and spin glass magnetic phases are found. Particular attention is given to obtaining a microscopic picture of the interplay between disorder and interaction-induced local moment formation, which underlies the metal-(gapless) insulator transition.

Collective excitation spectrum of a disordered Hubbard model

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.

A comment on `An important equation for the Anderson model'

We point out that a recent claim by Teng [Teng B 1995 J. Phys.: Condens. Matter 7 867] to have obtained a simple and exact solution of the single impurity Anderson model is incorrect.