LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XIV: Fourteenth Training Course in the Physics of Strongly Correlated Systems
1297(2010); http://dx.doi.org/10.1063/1.3518902View Description Hide Description
Narrow band materials (transition metals and rare‐earth elements compounds) often reveal anomalous physical properties. Their electronic structure is strongly renormalized by correlation effects due to Coulomb interaction between electrons. These effects can not be described by one‐electron approximation methods such as Density Functional Theory ( DFT ) and more elaborated approaches developed for many‐electron problems are needed here. In the present lectures we describe how to construct starting from DFT calculations the Hamiltonian in Wannier functions basis containing kinetic energy and Coulomb interaction terms and to solve the corresponding problem in static mean‐field approximation ( LDA +U method) and Dynamical Mean‐Filed Theory ( LDA +DMFT method). Application results for various real materials are presented.
1297(2010); http://dx.doi.org/10.1063/1.3518900View Description Hide Description
These lecture notes introduce quantum spin systems and several computational methods for studying their ground‐state and finite‐temperature properties. Symmetry‐breaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finite‐size scaling at continuous and first‐order phase transitions. Exact diagonalization and quantum Monte Carlo (stochastic series expansion) algorithms and their computer implementations are then discussed in detail. Applications of the methods are illustrated by results for some of the most essential models in quantum magnetism, such as the Heisenberg antiferromagnet in one and two dimensions, as well as extended models useful for studying quantum phase transitions between antiferromagnetic and magnetically disordered states.
1297(2010); http://dx.doi.org/10.1063/1.3518901View Description Hide Description
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean‐field picture as provided by Hartree‐Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott‐Hubbard metal‐insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean‐field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many‐body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean‐field theory for correlated fermions, the dynamical mean‐field theory (DMFT), (v) derive the DMFT self‐consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
1297(2010); http://dx.doi.org/10.1063/1.3518903View Description Hide Description
I show the exact solutions for the quantum compass model on a chain and ladder which are based on mapping to quantum Ising models in certain subspaces. I discuss the ground state and thermodynamic properties of both models. I show the spin transformation that maps quantum compass model to spin model and its applications to compass clusters of the sizes and I discuss the ground‐state and thermodynamic properties of these models.
1297(2010); http://dx.doi.org/10.1063/1.3518904View Description Hide Description
Ultra‐clean crystals of undergo a metamagnetic transition accompanied with a nematic phase at low temperatures for magnetic fields along the crystalline c‐axis. We show that the rotated O‐octahedra introduce a staggered spin‐orbit coupling which may be the cause for the absence of the nematic phase for fields parallel to the ‐layers.
de Haas‐van Alphen magnetization oscillations in the system of quasiparticles with spin dependent masses1297(2010); http://dx.doi.org/10.1063/1.3518905View Description Hide Description
We consider magnetic properties of a two‐dimensional Fermi liquid of quasiparticles with spin dependent masses, that are located in a periodic crystal potential. To determine thermodynamic properties of obtained Hofstadter‐like model we use the quantum transfer‐matrix method developed by T. Xiang and collaborators. The de Haas‐van Alphen oscillations of magnetization, as well as magnetic susceptibility are calculated at finite temperature.
1297(2010); http://dx.doi.org/10.1063/1.3518906View Description Hide Description
We discuss a paired state of quasiparticles with spin dependent masses (SDM), which were observed recently in the system (cf. Ref. ). In the same strongly‐correlated system the Fulde‐Ferrell‐Larkin‐Ovchinnikov (FFLO) phase appears. The spin‐dependent masses essentially extend the regime of applied field and temperatures in which FFLO phase is stable. We believe that the mechanism of the FFLO stabilization by the mass spin‐dependence is generic. Therefore, FFLO phases should be searched for in the same systems in which spin‐dependent masses were observed and vice versa. We compare results of our model calculations with the experiment.
1297(2010); http://dx.doi.org/10.1063/1.3518907View Description Hide Description
We study the influence of a unitary momentum‐dependent impurity potential on a two‐dimensional s‐wave superconducting order parameter in the real and the reciprocal space. The scattering process is considered in the t‐matrix approximation. We observe a significant difference in the effect on the order parameter induced by the isotropic and the momentum‐dependent parts of the scattering potential. Whereas the strong point impurity potential scattering leads to a strong on‐site suppression of superconductivity, the momentum‐dependent scattering influence is weak and extended beyond the impurity over the range of the order of magnitude of the coherence length. We also identify the wavevectors which determine the spatial modulation of the order parameter.
1297(2010); http://dx.doi.org/10.1063/1.3518908View Description Hide Description
We give a short overview of our approach, presented in detail in , for the ferromagnetic, three‐dimensional, translational‐symmetric Kondo lattice model which allows us to derive both magnon energies and linewidths (lifetimes) and to study the properties of the ferromagnetic phase at finite temperatures. Both anomalous softening and anomalous damping are obtained and discussed.
Experimental Signatures of Intrinsic Phase Separation in Magnetically Doped Two‐Dimensional Electron Gas1297(2010); http://dx.doi.org/10.1063/1.3518909View Description Hide Description
We theoretically study the properties of a recently observed inhomogeneous phase  preceding the metal‐insulator transition in Mn‐doped two‐dimensional electron gas (2DEG). We show that the competition between the carrier‐induced (ferromagnetic) double‐exchange interaction, and the anti‐ferromagnetic “super‐exchange” interaction of local Mn moments leads to an intrinsic phase separation (PS) at sufficiently low carrier density. Our results establish a dramatic effect of such a PS on the transport properties of the system, resulting in very strong (activated) temperature and magnetic field dependence, but anomalously weak density dependence of the resistivity under the PS dome—in striking agreement with experiments . Based on our results, we argue that such exotic transport behavior should be considered as a signature of intrinsic PS, in dramatic contrast to what is found in situations where PS is driven by disorder.