See also André-Marie Tremblay's introductory remarks and the talk of Th. Maier.

Michael Potthoff
Wednesday July 6 at 8:30

Cluster approximations are promising approaches to low-dimensional systems of correlated electrons. Starting from the grand potential as a functional of the self-energy, non-perturbative and thermodynamically consistent approximations can be constructed by constraining the search for stationary points. This idea is characteristic for the self-energy-functional theory (SFT). The SFT can be used as a general framework to classify different existing and to develop new quantum-cluster approaches. Different cluster schemes, including the cellular dynamical mean-field theory, the dynamical cluster approximation and the variational cluster-perturbation theory, will be discussed.

Gabriel Kotliar
Wednesday July 6 at 9:05

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
Wednesday July 6 at 10:35

We present a practical implementation of variational cluster perturbation theory and its application to the study of the interplay of d-wave superconductivity with antiferromagnetism in the two-dimensional Hubbard model close to half-filling. The band parameters include 2nd and 3rd neighbor hopping, which reveals the difference between hole and electron doping.

Sarma Kancharla
Wednesday July 6 at 12:10

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 angle-resolved photoemission experiments on electron- and hole-doped systems.

André-Marie Tremblay
Wednesday July 6 at 12:10

It is shown that the Two-Particle Self-Consistent 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 strong-coupling. Remarkable agreement with experiment is presented between TPSC and experiment for the electron-doped cuprates.

Andriana Moreo
Wednesday July 6 at 17:35

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
Thursday July 7 at 8:13

The pseudogap phase in the lightly hole-doped high-temperature 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 Ca2-xNaxCuO2Cl2 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
Thursday July 7 at 8:30

Atomic Resolution 'Mottness Mapping' in Ca2-xNaxCuO2Cl2

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 351-0198, Japan; [4] Department of Physics, University of California, Berkeley CA 94720 USA.; [5] Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8651, Japan

We recently began spectroscopic imaging STM studies of Ca2-xNaxCuO2Cl2. It is a beautifully simple high-Tc 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 hole-doping the Mott/Charge-Transfer insulating state (Meinders et al PRB 48, 3916 (1993)) by using asymmetry in high-voltage (~1V) tunneling spectroscopy (Anderson & Ong cond-mat/0405518; Randeria et al cond-mat/0412096). Based on these asymmetric tunneling models, we image the hole-density p with atomic resolution and find atomic-scale 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 Cu-O-Cu axes. At the atomic scale, the hole density arrangements strongly break local symmetry under 90-degree 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 so-called ‘incoherence’ of quasiparticle states near the zone-face and, (3) to the general lack of long range order in the zero-temperature electronic phase which intervenes between the M/C-T insulator and the superconductor in cuprates.

Arun Paramekanti
Thursday July 7 at 9:05

A supersolid phase of interacting bosons on the triangular lattice

We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half-filling, we provide evidence that (i) superfluidity survives for arbitrarily large repulsion and (ii) a supersolid phase emerges in the strongly correlated regime from an order-by-disorder mechanism. This is an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.

Erik Sorensen
Thursday July 7 at 14:35

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
Thursday July 7 at 15:10

Recent Neutron Scattering Studies of the Electron-Doped 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 electron-doped compound Nd$_{2-x}$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 field-effect results, we report on the doping-dependence of two-dimensional antiferromagnetic correlations in non-superconducting, oxygen-reduced NCCO in zero magnetic field, and compare the results to previous studies on as-grown 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).
[2] H.J. Kang et al., Nature 423, 522 (2003).
[3] K. Yamada et al., Phys. Rev. Lett. 90, 137004 (2003).
[4] E. Motoyama et al., unpublished.
[5] P.K. Mang et al, Phys. Rev. Lett. 93, 027002 (2004); E. Motoyama et al., unpublished.
[6] B. Kyung et al., Phys. Rev. Lett. 93, 147004 (2004); R.S. Markiewicz, Phys. Rev. B. 70, 174518 (2004).

Thursday July 7 at 16:45

We analyze a spin-pseudospin 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 super-antiferromagnetic (SAF) ground state. The theory of the spin-SAF transition in the coupled model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is proposed. The theory is applied for the much-discussed transition in the quarter-filled ladder compound $\rm NaV_2O_5$, where pseudospins represent its charge degrees of freedom. The estimates of the interladder spin-pseudospin interaction driving the spin-SAF 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 spin-SAF theory for $\rm NaV_2O_5$. Broader implications of the spin-SAF transition as an example of a new order emerging from spin-charge correlations and destruction of Ising's quantum critical point will be discussed.

Sandro Sorella
Friday July 8 at 8:30

We present a variational paradigm to understand the physical properties close to a Mott insulator state. The wave function is described by an uncorrelated mean-field state and by a singular density-density 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 holon-doblon bound state at arbitrary large temperature, whereas in 2D a Kosterlitz-Thouless 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 holon-doblon pairs. The relevance of such an unusual 2D Mott insulating state, for the phenomenology of underdoped High-Tc superconductors, is also discussed.

Peter Prelovsek
Friday July 8 at 9:05

Numerical approaches using the finite-temperature Lanczos method (FTLM) and recently developed micro-canonical 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 t-J 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 t-J model will be presented, and compared to experiments in cuprates.

Robert Eder
Friday July 8 at 10:00

We propose a many-body method for band-structure 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 d-shells is treated by exact diagonalization and the hopping between different atoms is treated by cluster perturbation theory.

We find good agreement between the calculated single-particle spectrum and angle resolved photoemission experiments in NiO.

Manuela Capello
Friday July 8 at 11:10

We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger 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
Critical behavior of the two-dimensional metal-insulator transition

The metal-insulator transition driven by electron interaction, the so-called Mott transition, is one of the most challenging issues in modern solid state physics, especially because of its possible connection with other phenomena, like high-temperature superconductivity.

John Hopkinson
Can RKKY mediated magnetism lead to novel physics on geometrically frustrated lattices?

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 corner-shared 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 well-defined spheroid of nearly degenerate (excited) spin states. Curiously, this feature holds only for certain special neighbour couplings--some of which correspond to the experimentally observed radius of the partially ordered state, raising the possibility that a direction-dependent RKKY interaction may be responsible for the unusual physics of MnSi under pressure

Sergei Isaksov
Ordering in Cs$_2$CuCl$_4$: Is there a proximate spin liquid?

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 spin-chirality and Neel correlations. We show how this may be tested in polarized neutron scattering experiments.

Fei Lin
Quantum Monte Carlo simulations of fullerene molecules

We will show some quantum Monte Carlo simulation results on the fullerene molecules based on the on-site hubbard model. The pair-binding 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 power-law correlations in the charge sector.

[cond-mat/0505710]