LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XII: Twelfth Training Course in the Physics of Strongly Correlated Systems
1014(2008); http://dx.doi.org/10.1063/1.2940446View Description Hide Description
These lecture notes give an introduction to quantum magnetism. We start by a discussion of paramagnetism and the Weiss meanfield theory applied to the Ising model. In the following sections, we turn to the fully quantum‐mechanical Heisenberg Hamiltonian. First, we consider the limit of small clusters whose properties we analyze via exact diagonalization. Bulk quantum magnets are then within the framework of the linear spinwave theory. A short discussion of Monte Carlo techniques follows. Finally, we discuss aspects of entanglement in quantum spin systems.
1014(2008); http://dx.doi.org/10.1063/1.2940445View Description Hide Description
We present a pedagogical discussions of the dynamical mean field (DMFA) and dynamical cluster (DCA) approximations and associated Monte Carlo and entropy‐based methods of Bayesian data analysis. The DMFA and DCA methods are developed as coarse‐graining approximations and the relationship between the cluster and lattice problems are detailed. The Hirsch‐Fye and continuous time Quantum Monte Carlo (QMC) algorithms are used to solve the cluster problem. The algorithms are discussed, together with methods for efficient measurements and the modifications required by the self‐consistency of the DMFA/DCA. Then, several principles of Bayesian data analysis are presented. When coupled with information theory, this analysis produces a precise and systematic way to analytically continue Matsubara‐time QMC results to real frequencies. We show how to use Bayesian inference to qualify the solution of the continuation and optimize the inputs. Besides developing the Bayesian formalism, we also present a detailed description of the data qualification, sketch an efficient algorithm to solve for the optimal spectra, give cautionary notes where appropriate, and present two detailed case studies to demonstrate the method.
1014(2008); http://dx.doi.org/10.1063/1.2940440View Description Hide Description
In these lecture notes, recent theoretical and experimental work on quantum phase transitions, in particular, in metals with strong electronic interactions will be reviewed. After an introduction to classical and quantum phase transitions, we will briefly discuss the standard model of metals, i.e., the Landau Fermi‐liquid theory, and routes to non‐Fermi‐liquid behavior. We will then focus on two different types of quantum phase transitions, magnetic quantum phase transitions in heavy‐fermion systems, and metal‐insulator transitions in heavily doped semiconductors.
1014(2008); http://dx.doi.org/10.1063/1.2940441View Description Hide Description
In the first part of these lecture notes we introduce the phenomenological equations for describing the heat and charge transport in thermoelectric samples. We discuss the solution obtained for various boundary conditions that are appropriate for the homogeneous and inhomogeneous thermoelectrics. In the second part we develop the formalism for a linear‐response many‐body description of the transport properties of correlated electrons. By properly determining the local heat‐current operator we show that the Jonson‐Mahan theorem applies to the Hamiltonians that are commonly used for the intermetallic compounds with Cerium, Europium and Ytterbium ions, so the various thermal‐transport coefficient integrands are related by powers of frequency. We illustrate how to use this formalism by calculating the thermoelectric properties of the periodic Anderson model and, then, show that these results explain the experimental data on heavy fermions and valence fluctuators. Finally, we calculate the thermoelectric properties of the Falicov‐Kimball model and use the results to explain the anomalous features of the intermetallic compounds in which one observes the valence‐change transition.
1014(2008); http://dx.doi.org/10.1063/1.2940442View Description Hide Description
The Hubbard (t‐U) model is the simplest model for studying strongly correlated systems. The t‐part of this model is the kinetic part and the U‐part is the interacting potential. In order to enhance the itinerancy of the kinetic part, some workers often include the hopping of the electrons to the next nearest neighbour (NNN) leading to the model. In this analytical study, we have developed from lattice diagrams, statistical distribution operators which simply by adding and subtracting one or two appropriately to sites in the basis states yield the same results as the kinetic part of the Hubbard Hamiltonian. By introducing the interacting Coulomb potential, we obtained the same ground state energies and wavefunctions for lattices in one dimension (1D), 2D and 3D as with the variational t‐U and models. The results and the implication of this equivalence are discussed with respect to magnetism and superconductivity
1014(2008); http://dx.doi.org/10.1063/1.2940443View Description Hide Description
Ground as well as excited state non‐linear optical properties of one‐dimensional Mott‐Hubbard insulators are discussed in detail. One dimensional strongly correlated materials are predicted to have several orders‐of‐magnitude larger excited state optical non‐linearities in comparison to that from the ground state. One dimensional strongly correlated materials like halogen bridged Ni compounds etc. have excited one‐ and two‐photon allowed states almost energetically degenerate which leads to order(s)‐of‐magnitude larger dipole coupling between them in comparison to that between the ground and optical state. This causes several orders‐of‐magnitude enhancement in the optical non‐linearities obtained from the first two‐photon state in the wavelength region suitable for terahertz communications. Our results and conclusions are based on exact numerical calculations of extended Hubbard model suitable strongly correlated systems. We also discuss ground state non‐linear properties like third‐harmonic generation, two‐photon absorption, electro‐absorption from the theoretical model and compare with experiments.
1014(2008); http://dx.doi.org/10.1063/1.2940444View Description Hide Description
We compare the role of the three‐site terms added to the t‐J models in the and the Ising cases in the extremely low doping regime, i.e. when a single hole added to the strongly interacting half‐filled system becomes a polaron. We show that in the realistic Ising case the three‐site terms play a vital role in the polaron movement and should never be neglected unlike in the case.