Abstract:
We determine the effect of an in-plane current flow on the critical properties of a 2d itinerant electron system near a ferromagnetic-paramagnetic quantum critical point. We study a model in which a nonequilibrium steady state is established as a result of exchange of particles and energy with an underlying substrate. the current $\vec{j}$ gives rise not only to an effective temperature equal to the voltage drop over a distance of order the mean free path, but also to symmetry breaking terms of the form $\vec{j}\cdot \vec{nabla}$ in the effective action. The effect of the symmetry breaking on the fluctuational and critical properties is found to be small although (in agreement with previous results) if rotational degrees of freedom are important, the current can make the classically ordered state dynamically unstable.

Abstract:
We present a method for solving impurity models with electron-phonon coupling, which treats the phonons efficiently and without approximations. The algorithm is applied to the Holstein-Hubbard model in the dynamical mean field approximation, where it allows access to strong interactions, very low temperatures and arbitrary fillings. We show that a renormalized Migdal-Eliashberg theory provides a reasonlable description of the phonon contribution to the electronic self energy in strongly doped systems, but fails if the quasiparticle energy becomes of order of the phonon frequency.

Abstract:
The nonequilibrium tunnelling center model of a localized electronic level coupled to a fluctuating two-state system and to two electronic reservoirs, is solved via an Anderson-Yuval-Hamann mapping onto a plasma of alternating positive and negative charges time-ordered along the two "Keldysh" contours needed to describe nonequilibrium physics. The interaction between charges depends both on whether their time separation is small or large compared to a dephasing scale defined in terms of the chemical potential difference between the electronic reservoirs and on whether their time separation is larger or smaller than a decoherence scale defined in terms of the current flowing from one reservoir to another. A renormalization group transformation appropriate to the nonequilibrium problem is defined. An important feature is the presence in the model of a new coupling, essentially the decoherence rate, which acquires an additive renormalization similar to that of the energy in equilibrium problems. The method is used to study interplay between the dephasing-induced formation of independent resonances tied to the two chemical potentials and the decoherence which cuts off the scaling and leads to effectively classical long-time behavior. We determine the effect of departures from equilibrium on the localization-delocalization phase transition.

Abstract:
To gain insight into the physics of the metal insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used one, two and four site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The cluster size dependence of the metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects start to occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences (in particular a sharper band edge) persist in the strong coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, and for differences in behavior between the single band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal insulator transition. Implications for the theoretical treatment of doped manganites are discussed.

Abstract:
Electronic phase behavior in correlated-electron systems is a fundamental problem of condensed matter physics. We argue here that the change in the phase behavior near the surface and interface, i.e., {\em electronic reconstruction}, is the fundamental issue of the correlated-electron surface or interface science. Beyond its importance to basic science, understanding of this behavior is crucial for potential devices exploiting the novel properties of the correlated systems. % We present a general overview of the field, and then illustrate the general concepts by theoretical studies of the model heterostructures comprised of a Mott-insulator and a band-insulator, which show that spin (and orbital) orderings in thin heterostructures are generically different from the bulk and that the interface region, about three-unit-cell wide, is always metallic, demonstrating that {\em electronic reconstruction} generally occurs. % Predictions for photoemission experiments are made to show how the electronic properties change as a function of position, and the magnetic phase diagram is determined as a function of temperature, number of layers, and interaction strength. Future directions for research are also discussed.

Abstract:
We present an efficient method for incorporating the dynamical effects of the screening of the Hubbard U by electronic degrees of freedom in the solid into the single site dynamical mean field approximation. The formalism is illustrated by model system calculations which capture the essential features of the frequency dependent interactions proposed for Gd, Ni, SrVO_3 and other compounds. Screening leads to shifts in the metal-insulator phase boundary, changes in the spectral function near the Mott-Hubbard gap edge and to a renormalization of the quasiparticle weight. Hubbard bands are generically neither separated by the screened nor the unscreened interaction energy, implying that the common practice of extracting the Hubbard U from the energies of features in photoemission and inverse photoemission spectra requires reexamination.

Abstract:
A theoretical model is proposed for the (0,0,1) superlattice manganite system (LaMnO$_3$)$_n$(SrMnO$_3$)$_m$. The model includes the electron-electron, electron-phonon, and cooperative Jahn-Teller interactions. It is solved using a version of single-site the dynamical mean field approximation generalized to incorporate the cooperative Jahn-Teller effect. The phase diagram and conductivities are calculated. The behavior of the superlattice is found to a good approximation to be an average over the density-dependent properties of individual layers, with the density of each layer fixed by electrostatics.

Abstract:
We compare the interaction parameters measured on LaMnO$_3$ to single site dynamical mean field estimates of the critical correlation strength needed to drive a Mott transition, finding that the total correlation strength (electron-electron plus electron-lattice) is very close to but slightly larger than the critical value, while if the electron lattice interaction is neglected the model is metallic. Our results emphasize the importance of additional physics including the buckling of the Mn-O-Mn bonds.

Abstract:
A comprehensive theoretical model for the bulk manganite system La$_{1-x}$(Ca,Sr)$_x$MnO$_3$ is presented. The model includes local and cooperative Jahn-Teller distortions and the on-site Coulomb and exchange interaction. The model is is solved in the single-site dynamical mean field approximation using a solver based on the semiclassical approximation. The model semi-quantitatively reproduces the observed phase diagram for the doping $0 \leq x<0.5$ and implies that the manganites are in the strong coupling region but close to Mott insulator/metal phase boundary. The results establish a formalism for use in a broader range of calculations, for example on heterostructures.

Abstract:
The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be unstable to large-amplitude but purely local fluctuations. The instability is shown to arise either from phase separation or, in a narrow parameter regime, from the presence of a competing phase. The instability is therefore suggested as a computationally inexpensive means of locating regimes of parameter space in which phase separation occurs.