


See also AndréMarie Tremblay's introductory remarks and the talk of Th. Maier.
Michael Potthoff Quantumcluster theories from a variational perspective Cluster approximations are promising approaches to lowdimensional systems of correlated electrons. Starting from the grand potential as a functional of the selfenergy, nonperturbative and thermodynamically consistent approximations can be constructed by constraining the search for stationary points. This idea is characteristic for the selfenergyfunctional theory (SFT). The SFT can be used as a general framework to classify different existing and to develop new quantumcluster approaches. Different cluster schemes, including the cellular dynamical meanfield theory, the dynamical cluster approximation and the variational clusterperturbation theory, will be discussed.
Gabriel Kotliar Cluster methods My group will prepare two half hour presentations , one is a critical overview of our results which interprets the cluster results from a strong coupling perspective which will highlight the features which are close to RVB (I will coordinate this with Bumsoo for any possible overalp or incongruency ). The second will discuss the technical issues underlying the foundations of the approach, convergence as a function of size, Weiss field functionals, discretizations, periodizations etc. Here I will compare the technical issues faced in solving the CDMFT euqations with the same problems we had solving the single site DMFT equations and how they were overcome in the single site case, hoping that it will inspire similar developments for the cluster case.
David Sénéchal Variational cluster perturbation theory and superconductivity in the Hubbard model We present a practical implementation of variational cluster perturbation theory and its application to the study of the interplay of dwave superconductivity with antiferromagnetism in the twodimensional Hubbard model close to halffilling. The band parameters include 2nd and 3rd neighbor hopping, which reveals the difference between hole and electron doping.
Sarma Kancharla Superconductivity in the 2D Hubbard model The $d$wave superconducting (SC) phase in the two dimensional Hubbard model is investigated using Cellular Dynamical Mean Field Theory. The SC order parameter is found to assume a dome shape as a function of doping and scale like the magnetic exchange coupling $J$ for $U$ comparable to the bandwidth, whereas, the SC gap reduces monotonically with increasing doping. SC sets in only at a finite doping and is driven by a lowering of kinetic energy rather than potential energy in conformity with experiments on cuprates. We also account for the observed asymmetry in angleresolved photoemission experiments on electron and holedoped systems.
AndréMarie Tremblay Concordance between weak and strong coupling approaches at intermediate coupling It is shown that the TwoParticle SelfConsistent Approach (TPSC), that works best at weak coupling, gives, at intermediate coupling, several results that are in agreement with approaches such as Cluster Perturbation Theory and Dynamical Cluster Approximation, that work best at strongcoupling. Remarkable agreement with experiment is presented between TPSC and experiment for the electrondoped cuprates.
Andriana Moreo Complexity as a Result of Competing Orders in Correlated Materials Strongly correlated systems with magnetic, charge and lattice degrees of freedom are studied using numerical techniques. Complex phases arising as a result of competing orders will be presented. The experimental consequences of such inhomogeneous states will be discussed. The presentation will focus on transition metal oxides, such as high Tc cuprates and manganites, and dilute magnetic semiconductors.
Christian Lupien A 'checkerboard' electronic crystal state in lightly holedoped NaCCOC The pseudogap phase in the lightly holedoped hightemperature superconductors is rich in peculiar phenomena which may be closely related to the strong correlation effects in cuprates. We have carried out scanning tunneling microscopy/spectroscopy (STM/STS) on Ca2xNaxCuO2Cl2 single crystals (x = 0.08  0.12) to visualize the spatial variation of the electronic states in the zero temperature pseudogap phase. We found 'checkerboard' local density of states (LDOS) modulation which is characterized by the tiling of the commensurate 4ax4a electronic entity. Each 4ax4a unit cell carries intricate internal structures which include 4a/3 x 4a/3 LDOS modulation. The modulation amplitudes of these components are strongly energy dependent but the periodicities are energy independent.
J.S. Séamus Davis Atomic Resolution 'Mottness Mapping' in Ca2xNaxCuO2Cl2 Y. Kohsaka[1], C.Taylor[1], C. Lupien[2], T. Hanaguri[3], D.H. Lee[4], H. Takagi[3,5] & J. C. Séamus Davis[1] [1] LASSP, Department of Physics, Cornell University, Ithaca, NY 14853, USA; [2] Département de Physique, U. de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada.; [3] Magnetic Materials Laboratory, RIKEN, Wako, Saitama 3510198, Japan; [4] Department of Physics, University of California, Berkeley CA 94720 USA.; [5] Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 2778651, Japan We recently began spectroscopic imaging STM studies of Ca2xNaxCuO2Cl2. It is a beautifully simple highTc crystal, with only one CuO2 plane in the unit cell and an undistorted crystal structure, which can be doped from the insulating to the superconductive states. We measure the spectral weight shifts due to holedoping the Mott/ChargeTransfer insulating state (Meinders et al PRB 48, 3916 (1993)) by using asymmetry in highvoltage (~1V) tunneling spectroscopy (Anderson & Ong condmat/0405518; Randeria et al condmat/0412096). Based on these asymmetric tunneling models, we image the holedensity p with atomic resolution and find atomicscale variations ranging 9% < p <15% for samples with mean value of p=12% The spatial arrangements of p have no long range order but reveal intense 2a0X1a0 correlations and weaker 4a0X4a0 correlations, at very short distances. Embedded in this electronically disordered background, small more ordered regions of dimensions ~4a0X16a0, (which we refer to as ‘dominoes’) are sometimes found  with equal probability of orientation along both crystalline CuOCu axes. At the atomic scale, the hole density arrangements strongly break local symmetry under 90degree rotations along the bonds between Cu atoms, but in a random fashion which looks something like a ‘quantum labyrinth’. We discuss the relationship of these observations to (1) the ‘cluster spin glass’ phenomenology deduced from NMR, NQR, muSR, and INS, (2) the socalled ‘incoherence’ of quasiparticle states near the zoneface and, (3) to the general lack of long range order in the zerotemperature electronic phase which intervenes between the M/CT insulator and the superconductor in cuprates.
Arun Paramekanti A supersolid phase of interacting bosons on the triangular lattice We study the interplay of Mott localization, geometric frustration, and superfluidity for hardcore bosons with nearestneighbor repulsion on the triangular lattice. For this model at halffilling, we provide evidence that (i) superfluidity survives for arbitrarily large repulsion and (ii) a supersolid phase emerges in the strongly correlated regime from an orderbydisorder mechanism. This is an unusual example of a stable supersolid phase of hardcore lattice bosons at a commensurate filling.
Erik Sorensen Manifestations of the Kondo Polaron The Kondo polaron (screening cloud) is indirectly observable in quantum dot, mettalic and purely magnetic systems. The presence of a Kondo impurity will for example strongly modify the persistent current flowing in a mesoscopic ring. I will present parallel DMRG and exact diagonalization studies of the kondo polaron as it occurs in these systems. In some cases the results can be compared to quantum cluster calculations.
Martin Greven Recent Neutron Scattering Studies of the ElectronDoped Superconductor (Nd,Ce)$_2$CuO$_4$ Superconductivity in the cuprates occurs in close proximity to antiferromagnetic phases, and determining the nature of these phases is essential in arriving at a satisfactory understanding of these complex oxides. A unique opportunity exists in the prototypical electrondoped compound Nd$_{2x}$Ce$_x$CuO$_4$ (NCCO), for which the upper critical field is relatively small ($\sim 10$ T) and thus attainable at scattering facilities. Although a magnetic field enhances the elastic response at the antiferromagnetic position $(\pi,\pi)$, it has been shown [1] that this effect is the paramagnetic response of the epitaxial secondary phase (Nd,Ce)$_2$O$_3$, and not due to the emergence of a new exotic magnetic phase, as originally claimed [2]. However, our recent inelastic neutronscattering results, on large crystals grown at Stanford University, demonstrate a real field effect on the magnetic excitations at $(\pi,\pi)$. It is known that in NCCO, these excitations become gapped below $T_c$ [3]. Here, we report on the effect of a magnetic field on this gap [4]. In addition to these fieldeffect results, we report on the dopingdependence of twodimensional antiferromagnetic correlations in nonsuperconducting, oxygenreduced NCCO in zero magnetic field, and compare the results to previous studies on asgrown NCCO [5] as well as with recent theoretical predictions for the Hubbard model [6].
[1] P.K. Mang et al, Nature 426, 139 (2003); Phys. Rev. B 70, 094507 (2004).
Gennady Y. Chitov The spinSAF transition in the quarterfilled ladder compound $\rm NaV_2O_5$ We analyze a spinpseudospin model comprised of the frustrated quantum Ising model coupled to the Heisenberg spin chains in a particular region of interactions, corresponding to the Ising sector's superantiferromagnetic (SAF) ground state. The theory of the spinSAF transition in the coupled model into a phase with coexistent SAF Ising (pseudospin) longrange order and a spin gap is proposed. The theory is applied for the muchdiscussed transition in the quarterfilled ladder compound $\rm NaV_2O_5$, where pseudospins represent its charge degrees of freedom. The estimates of the interladder spinpseudospin interaction driving the spinSAF transition along with several other microscopic parameters are obtained by exactly diagonalizing appropriate clusters of the underlying generalized Hubbard Hamiltonian. The results allow us to claim the quantitative applicability of the spinSAF theory for $\rm NaV_2O_5$. Broader implications of the spinSAF transition as an example of a new order emerging from spincharge correlations and destruction of Ising's quantum critical point will be discussed.
Sandro Sorella Critical behavior near a two dimensional Mott insulator We present a variational paradigm to understand the physical properties close to a Mott insulator state. The wave function is described by an uncorrelated meanfield state and by a singular densitydensity Jastrow factor, required for the correct low momentum behavior of the charge correlations. Within this framework, the physical ground state quantities described by this variational ansatz, are mapped onto finite temperature classical averages of a neutral Coulomb gas model in arbitrary dimensions, the positive charges correspond to the sites with doubly occupied sites (doblons) and the negative ones to the empty sites (holons). In one dimension this model displays always a confined dielectric phase with a holondoblon bound state at arbitrary large temperature, whereas in 2D a KosterlitzThouless transition between a high temperature plasma phase with perfect screening and a confined low temperature dielectric phase is found. In the quantum analog described by our variational ansatz the inverse temperature corresponds to the strength of the correlation factor. Thus in one dimension we reproduce the known Mott insulating phase for arbitrary small value of the correlation strength and we obtain in this way all the known low energy properties of the Bethe ansatz exact solution of the Hubbard model at half filling. In two dimension the situation is much more interesting, because with the same ansatz, following the correspondence with the classical model, we predict (and verify numerically by quantum Monte Carlo) that the Mott insulating state appears only for large enough strength of the correlation, whereas below a critical value a charged metallic phase is stabilized with a plasmon gap and Friedel oscillations. The Mott insulating state is characterized by several unconventional properties in two dimensions, that can be realized even in presence of magnetic order, because the critical behavior is determined by the singular interaction between the charges, and not between the electron spins. Due to this singular interaction the quasiparticle weight may vanish with non universal power laws. Moreover charge correlations decay algebraically with large exponent (> 4) due to a residual dipole interaction between holondoblon pairs. The relevance of such an unusual 2D Mott insulating state, for the phenomenology of underdoped HighTc superconductors, is also discussed.
Peter Prelovsek Finite temperature dynamics of small correlated electron systems: anomalous properties of cuprates Numerical approaches using the finitetemperature Lanczos method (FTLM) and recently developed microcanonical Lanczos method will be described, which are particularly adapted to study dynamical properties of correlated electrons on small systems at finite temperatures. Cuprates are the challenging example of materials with strongly correlated electrons. At least in the normal state their anomalous properties can be well accounted for within the tJ model. As an application of the FTLM recent results for transport properties, in particular the resistivity and optical conductivity, and the spin response within the tJ model will be presented, and compared to experiments in cuprates.
Robert Eder Cluster perturbation theory for transition metal oxides  the correlated band structure of NiO We propose a manybody method for bandstructure calculations for strongly correlated electron systems and apply it to transition metal oxides with NiO as an example. The method may be viewed as an application of cluster perturbation theory to a realistic model of a transition metal oxide whereby the Coulomb interaction within the transition metal dshells is treated by exact diagonalization and the hopping between different atoms is treated by cluster perturbation theory. We find good agreement between the calculated singleparticle spectrum and angle resolved photoemission experiments in NiO.
Manuela Capello We show that a particular class of variational wave functions reproduces the lowenergy properties of the Hubbard model in one dimension. Our approach generalizes to finite onsite Coulomb repulsion the fullyprojected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttingerliquid behavior of the doped $t{}J$ model. Within our approach, the longrange Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the longdistance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct powerlaw behavior of the correlation functions, with the exponents predicted by the TomonagaLuttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small$q$ part of the Jastrow factor.
Federico Becca The metalinsulator transition driven by electron interaction, the socalled Mott transition, is one of the most challenging issues in modern solid state physics, especially because of its possible connection with other phenomena, like hightemperature superconductivity.
John Hopkinson Despite recent progress toward understanding geometrically frustrated magnetism in insulating compounds, (geometrical factors from degenerate spin structures explain diffuse neutron scattering patterns), the prospect of similar physics arising in metallic magnetic systems does not seem to have gained much attention. Neutron scattering experiments have started to provide us with some intriguing puzzles, including a "partially ordered state" in MnSi coincident with the vanishing of the helimagnetic ordered state under pressure, and the mysterious "butterfly" pattern observed in CeCu_5.9Au_0.1. In this poster we take the first steps toward the development of an RKKY description of MnSi by solving the classical Heisenberg model at the mean field level on the cornershared triangle lattice of the magnetic Mn sites. For this simplified model we find an ordering wavevector along q00 (and equivalent directions) delineating a 120^o rotated classical ground state. The locus of low energy wavevectors lies on a welldefined spheroid of nearly degenerate (excited) spin states. Curiously, this feature holds only for certain special neighbour couplingssome of which correspond to the experimentally observed radius of the partially ordered state, raising the possibility that a directiondependent RKKY interaction may be responsible for the unusual physics of MnSi under pressure
Sergei Isaksov The frustrated antiferromagnet Cs$_2$CuCl$_4$ has several interesting properties that have been suggested as evidence of its proximity to a two dimensional quantum spin liquid. We study a concrete version of this proposal in the framework of the O(4) invariant critical theory [A. V. Chubukov, S. Sachdev and T. Senthil, Nucl. Phys. B 426, 601 (1994)] that describes the quantum phase transition between a spiral magnetic state and a spin liquid state with gapped bosonic spinons. Direct numerical calculation of the anomalous exponent in spin correlations shows that the critical scattering has broad continua qualitatively similar to experiment. More remarkably we show that the enlarged O(4) symmetry leads to the same power law decay for the vector spinchirality and Neel correlations. We show how this may be tested in polarized neutron scattering experiments.
Fei Lin We will show some quantum Monte Carlo simulation results on the fullerene molecules based on the onsite hubbard model. The pairbinding energies are calculated and compared with second order perturbation theory results. Our simulations show an agreement with Hund's rule. We introduce a variational paradigm to understand the Mott transition in two dimensions, relevant for a wide class of correlated materials. Within this framework, electrons strongly interact with collective plasmon excitations that induce critical properties. We predict anomalous properties on either sides of the transition. In particular, the quasiparticle weight vanishes both in the metallic and in the Mott insulating phase. Finally, we predict that the Mott phase, although gapped, presents powerlaw correlations in the charge sector. [condmat/0505710]
