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LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS X: Tenth Training Course in the Physics of Correlated Electron Systems and High Tc Superconductors Date: 3-14 October 2005 Location: Salerno (Italy) ISBN: 0-7354-0340-6 Editor(s): Ferdinando Mancini, Adolfo Avella

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Strongly Correlated Electron Behaviors and Heavy Fermions in Anomalous Rare‐earth and actinide Systems

B. Coqblin

AIP Conf. Proc. 846, pp. 3-93; doi:http://dx.doi.org/10.1063/1.2222266 (91 pages)

Online Publication Date: 7 July 2006

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After an introduction on the different cases of anomalous rare‐earth systems, we start to present the case of intermediate valence, with the example of the phase diagram of Cerium and the study of the Anderson Hamiltonian. Then, we discuss the Kondo effect for a single impurity, with a perturbation calculation above the Kondo temperature and the exact single‐impurity solution showing a heavy fermion behaviour below it. Then, the Kondo effect for Ce, Yb and other anomalous rare‐earth impurities and their different transport properties arc discussed, with in particular a description of the Schrieffer‐Wolff transformation and of the “Coqblin‐Schrieffer” Hamiltonian without and with crystalline field effects. The properties of actinide metals and compounds are also discussed and both the spin fluctuation model applied to Plutonium or Neptunium metals or compounds and the undercreened Kondo‐lattice model applied to Uranium Kondo and ferromagnetic compounds are presented. The Kondo‐lattice problem is also discussed, with a special emphasis on the Doniach diagram, the mean‐field approximations, the competition between the Kondo effect and the magnetic order, the spin glass‐Kondo competition and the multi‐channel Kondo effect. A brief summary of the superconductivity occurring in Ce, U or even Pu systems is finally presented. © 2006 American Institute of Physics
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71.27.+a Strongly correlated electron systems; heavy fermions
72.15.Qm Scattering mechanisms and Kondo effect
71.55.Ak Metals, semimetals, and alloys

Strong Correlations in Low Dimensional Systems

T. Giamarchi

AIP Conf. Proc. 846, pp. 94-129; doi:http://dx.doi.org/10.1063/1.2222267 (36 pages) | Cited 1 time

Online Publication Date: 7 July 2006

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I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)‐Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given. © 2006 American Institute of Physics
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71.27.+a Strongly correlated electron systems; heavy fermions
71.30.+h Metal-insulator transitions and other electronic transitions

Functional Renormalization Group Approach to Correlated Electron Systems

Walter Metzner

AIP Conf. Proc. 846, pp. 130-161; doi:http://dx.doi.org/10.1063/1.2222268 (32 pages)

Online Publication Date: 7 July 2006

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The functional renormalization group is an ideal tool for dealing with the diversity of energy scales and competition of correlations in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Suitable truncations of the hierarchy have recently led to powerful new approximation schemes. I derive and discuss the structure of the flow equations for several versions of the functional renormalization group. I then review applications of truncated flow equations to the two‐dimensional Hubbard model, focussing in particular on magnetic correlations and d‐wave superconductivity, and to one‐dimensional Luttinger liquids with impurities, where a strikingly simple truncation captures a surprising amount of non‐trivial correlation effects. © 2006 American Institute of Physics
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71.27.+a Strongly correlated electron systems; heavy fermions
71.10.Fd Lattice fermion models (Hubbard model, etc.)
74.20.Mn Nonconventional mechanisms

Numerical Approaches to Coupled Quantum Systems

Wolfgang von der Linden

AIP Conf. Proc. 846, pp. 162-217; doi:http://dx.doi.org/10.1063/1.2222269 (56 pages)

Online Publication Date: 7 July 2006

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Computational physics has proven to be highly successful in revealing valuable insight into strongly correlated many body systems. The purpose of this lecture is threefold. Firstly, we present ubiquitous model hamiltonians tailored to describe different constituents of strongly correlated many body systems individually. Secondly, a collection of modern numerical techniques, currently employed to study such models, is discussed in great detail to provide insight into the pros and cons of these approaches. Finally, we will apply these numerical approaches to coupled quantum systems ‘the manganites’ and study some of their fascinating features. © 2006 American Institute of Physics
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71.27.+a Strongly correlated electron systems; heavy fermions
74.70.-b Superconducting materials other than cuprates

Is Room‐temperature Superconductivity with Phonons Possible?

M. de Llano and M. Grether

AIP Conf. Proc. 846, pp. 221-235; doi:http://dx.doi.org/10.1063/1.2222270 (15 pages)

Online Publication Date: 7 July 2006

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By recognizing the vital importance of two‐hole Cooper pairs (CPs) in addition to the usual two‐electron ones in a strongly‐interacting many‐electron system, the concept of CPs was re‐examined with striking conclusions: namely, they are gapped and linearly‐dispersive resonances with a finite lifetime—but provided the ideal‐gas Fermi sea is replaced by a BCS‐correlated unperturbed ground‐state “sea.” Based on this, Bose‐Einstein condensation (BEC) theory has been generalized to include not boson‐boson interactions (also neglected in BCS theory) but rather boson‐fermion (BF) interaction vertices reminiscent of the Fröhlich electron‐phonon interaction in metals. Instead of phonons, the bosons in the generalized BEC (GBEC) theory are now both particle and hole CPs. Unlike BCS theory, the GBEC model is not a mean‐field theory restricted to weak‐coupling as it can be diagonalized exactly. In weak coupling it reproduces the BCS condensation energy, and the next‐order‐in‐coupling term increases its magnitude with respect to BCS. Each kind of CP is responsible for only half the condensation energy. The GBEC theory reduces to all the old known statistical theories as special cases—including the so‐called “BCS‐Bose crossover” picture which in turn generalizes BCS theory by not assuming that the interelectronic chemical potential equals the Fermi energy. Indeed, a BCS condensate is precisely the weak‐coupling limit of a GBE condensate with equal numbers of both types of CPs. With feasible Cooper/BCS model interelectonic interaction parameter values, and even without BF interactions, the GBEC theory yields transition temperatures [including room‐temperature superconductivity (RTSC)] substantially higher than the BCS ceiling of around 45K, without relying on non‐phonon dynamics involving excitons, plasmons, magnons or otherwise purely‐electronic mechanisms. The results are expected to shed light on the experimental search for RTSC. © 2006 American Institute of Physics
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71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems
71.10.Li Excited states and pairing interactions in model systems
74.20.Fg BCS theory and its development
71.27.+a Strongly correlated electron systems; heavy fermions

Fermionic Renormalization Group Flow at All Scales: Breaking a Discrete Symmetry

Roland Gersch, Carsten Honerkamp, Daniel Rohe, and Walter Metzner

AIP Conf. Proc. 846, pp. 236-244; doi:http://dx.doi.org/10.1063/1.2222271 (9 pages)

Online Publication Date: 7 July 2006

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We extend the functional renormalization group technique in a modi cation of the one‐particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry‐broken phase of a charge‐density wave mean‐ eld model. We study the half‐ lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry‐breaking eld allows us to access the symmetry‐broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature. © 2006 American Institute of Physics
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71.45.Lr Charge-density-wave systems
71.10.Fd Lattice fermion models (Hubbard model, etc.)

How to Calculate Correlation Functions of Heisenberg Chains

Rob Hagemans, Jean‐Sébastien Caux, and Jean Michel Maillet

AIP Conf. Proc. 846, pp. 245-254; doi:http://dx.doi.org/10.1063/1.2222273 (10 pages) | Cited 2 times

Online Publication Date: 7 July 2006

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We describe a method for calculating dynamical spin‐spin correlation functions in the isotropic and anisotropic antiferromagnetic Heisenberg models. Our method is able to produce results with high accuracy over the full parameter space. © 2006 American Institute of Physics
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75.10.Pq Spin chain models

Extending the Theory of Phonon‐mediated Superconductivity in quasi‐2D

J. P. Hague

AIP Conf. Proc. 846, pp. 255-264; doi:http://dx.doi.org/10.1063/1.2222274 (10 pages)

Online Publication Date: 7 July 2006

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I present results from an extended Migdal‐Eliashberg theory of electron‐phonon interactions and superconductivity. The history of the electron‐phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenberg’s theorem, the Bardeen‐Cooper‐Schrieffer theory and Coulomb repulsion. © 2006 American Institute of Physics
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74.20.Fg BCS theory and its development
74.25.Kc Phonons
71.38.-k Polarons and electron-phonon interactions

Bond Order in the Stripe Phase of Cuprates at the Hole Doping Level 1/8

A. Macia̧g and P. Wróbel

AIP Conf. Proc. 846, pp. 265-274; doi:http://dx.doi.org/10.1063/1.2222275 (10 pages)

Online Publication Date: 7 July 2006

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We investigate the formation of bond order in the stripe phase of cuprates. We use a combination of the bond and the spin polaron formalism together with the recursion method to evaluate and compare the energy of several different spin backgrounds in the framework of the t‐J model (tJM) on the square lattice. We find out that the stripe system, in which antiferromagnetic (AF) ordered domains are separated by two‐leg ladder‐like bond ordered domain walls (DWs) with singlets formed on legs, is stable at and above the hole doping level 1/8. This fact seems to be relevant to the nature of high‐energy excitations recently observed in neutron‐scattering experiments on cuprates. © 2006 American Institute of Physics
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74.20.Mn Nonconventional mechanisms
71.10.Fd Lattice fermion models (Hubbard model, etc.)
74.72.-h Cuprate superconductors

Transport Properties in Bilayer Quantum Hall Systems in the Presence of a Topological Defect

Gerardo Cristofano, Vincenzo Marotta, Adele Naddeo, and Giuliano Niccoli

AIP Conf. Proc. 846, pp. 275-284; doi:http://dx.doi.org/10.1063/1.2222276 (10 pages)

Online Publication Date: 7 July 2006

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Following a suggestion given in [1], we show how a bilayer Quantum Hall system at fillings v  =  math can exhibit a point‐like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings which evidence the presence of a topological defect in the transport properties of the bilayer system. © 2006 American Institute of Physics
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72.10.Fk Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect)
73.43.Cd Theory and modeling

Orbital Driven Spin Ordering in the One Dimensional Chains of Titanium Pyroxene

Jasper van Wezel and Jeroen van den Brink

AIP Conf. Proc. 846, pp. 285-294; doi:http://dx.doi.org/10.1063/1.2222277 (10 pages)

Online Publication Date: 7 July 2006

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In this paper we present a model description of the one dimensional titanium chains found in titanium pyroxene. The model we present can be used to understand the available experimental data regarding the magnetic and the lattice properties of the compound, as well as account for the conflicting results found in different calculational approaches. From this work we conclude that a novel type of ‘orbital Peierls’ transition occurs in the chains of NaTiSi2O6. © 2006 American Institute of Physics
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75.10.Pq Spin chain models
75.25.-j Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source x-ray scattering, etc.)
75.30.Kz Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.)

Double exchange model for correlated electrons in systems with t2g orbital degeneracy

Krzysztof Wohlfeld

AIP Conf. Proc. 846, pp. 295-303; doi:http://dx.doi.org/10.1063/1.2222278 (9 pages)

Online Publication Date: 7 July 2006

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We formulate the double exchange (DE) model for systems with t2g orbital degeneracy, relevant for hole‐doped cubic vanadates. In the relevant regime of strong on‐site Coulomb repulsion U we solve the model using two distinct mean‐field approximations: Hartree‐Fock, and mean‐field applied to the formulation of the model in the Kotliar‐Ruckenstein slave boson represenation. We show how, due to the relative weakness of the DE mechanism via t2g degenerate orbitals, the anisotropic C‐type antiferromagnetic metallic phase and the orbital liquid state can be stabilized. This is contrasted with the DE mechanism via eg degenerate orbitals which stabilizes the ferromagnetic order in the hole‐doped regime of manganites. The obtained results are in striking agreement with the observed magnetic structures and the collapse of the orbital order in the doped La1−xSrxVO3, Pr1−xCaxVO3 and Nd1−xSrxVO3. © 2006 American Institute of Physics
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71.27.+a Strongly correlated electron systems; heavy fermions
71.70.Gm Exchange interactions
75.30.Et Exchange and superexchange interactions
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