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The surprising inversion of the orbital- and magnetic-order transition temperatures in the RVO3 series with increasing the rare-earth radius makes the series unique among orbitally-ordered materials. Here, augmenting dynamical mean-field theory with a decomposition of the order parameter into irreducible tensors, we show that this anomalous behavior emerges from an unusual hierarchy of interactions. First, increasing the rare-earth radius, orbital physics comes to be controlled by xz-xz quadrupolar super-exchange rather than by lattice distortion. Next, for antiferromagnetic spin order, orbital super-exchange terms with different spin rank compete, so that the dipolar spin-spin interaction dominates. Eventually, G-type magnetic order (anti-ferro in all directions) can appear already above the orbital ordering transition, and C-type order (anti-ferro in the ab plane) right around it. The strict constraints we found explain why the inversion is rare, giving at the same time criteria to look for similar behavior in other materials., Comment: 5 pages, 4 figures; submitted on 25 Oct 2024

We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the way the spectra are sampled. Our derivation also suggests a modification of R\'enyi entropy, giving it a non-trivial $\eta\to0$ limit. We show that the sharper peaks generally obtained in ASM are associated with entropies of order $\eta<1$. Our work provides a generalization of the maximum entropy method that enables extracting more structure than the traditional method., Comment: 5 pages, 1 figure

Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed. This paper explores a regularization method based on the repeated application of Tikhonov regularization under the discrepancy principle. The method can be readily implemented in any linear algebra package and gives results surprisingly close to the maximum entropy method (MaxEnt). We analyze the method in detail and demonstrate its connection to MaxEnt. In addition, we provide a straightforward method for estimating the noise level of QMC data, which is helpful for practical applications of the discrepancy principle when the noise level is not known reliably., Comment: 12 pages, 10 figures

We show that the $t_{2g}^2$ perovskite LaVO$_3$, in its orthorhombic phase, is a rare case of a system hosting an orbital-ordering Kugel-Khomskii phase transition, rather than being controlled by the Coulomb-enhanced crystal-field splitting. We find that, as a consequence of this, the magnetic transition is close to (and even above) the super-exchange driven orbital-ordering transition, whereas typically magnetism arises at much lower temperatures than orbital ordering. Our results support the experimental scenario of orbital-ordering and G-type spin correlations just above the monoclinic-to-orthorhombic structural change. To explore the effects of crystal-field splitting and filling, we compare to YVO$_3$ and $t_{2g}^1$ titanates. In all these materials the crystal-field is sufficiently large to suppress the Kugel-Khomskii phase transition., Comment: 5 pages, 5 figures

Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating over all non-negative spectra weighted by how well they fit the data. In a recent paper, we found that discretizing the functional integral as in Feynman's path-integrals, does not have a well-defined continuum limit. Instead, the limit depends on the discretization grid whose choice may strongly bias the results. In this paper, we demonstrate that sampling the grid points, instead of keeping them fixed, also changes the functional integral limit and rather helps to overcome the bias considerably. We provide an efficient algorithm for doing the sampling and show how the density of the grid points acts now as a default model with a significantly reduced biasing effect. The remaining bias depends mainly on the width of the grid density, so we go one step further and average also over densities of different widths. For a certain class of densities, including Gaussian and exponential ones, this width averaging can be done analytically, eliminating the need to specify this parameter without introducing any computational overhead., Comment: 10 pages, 10 figures

The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible spectral functions, weighted by how well they fit the data. Its main advantage is the apparent lack of adjustable parameters and smoothness constraints, using instead the information on the statistical noise in the data. Its main disadvantage is the enormous computational cost of performing the functional integral. Here we introduce an efficient implementation, based on the singular value decomposition of the integral kernel, eliminating this problem. It allows us to analyze the behavior of the average spectrum method in detail. We find that the discretization of the real-frequency grid, on which the spectral function is represented, biases the results. The distribution of the grid points plays the role of a default model while the number of grid points acts as a regularization parameter. We give a quantitative explanation for this behavior, point out the crucial role of the default model and provide a practical method for choosing it, making the average spectrum method a reliable and efficient technique for analytic continuation., Comment: 12 pages, 10 figures

Ginzburg-Landau theory describes phase transitions as the competition between energy and entropy: The ordered phase has lower energy, while the disordered phase has larger entropy. When heating the system, ordering is reduced entropically until it vanishes at the critical temperature. This established picture implicitly assumes that the energy difference between ordered and disordered phase does not change with temperature. We show that for the Mott insulator KCuF3 this assumption is strongly violated: thermal expansion energetically stabilizes the orbitally-ordered phase to such and extent that no phase transition is observed. This new mechanism explains not only the absence of a phase transition in KCuF3 but even suggests the possibility of an inverted transition in closed-shell systems, where the ordered phase emerges only at high temperatures., Comment: 5 pages, 5 figures

We study the origin of the cubic to tetragonal and tetragonal to monoclinic structural transitions in KCrF3, and the associated change in orbital order, paying particular attention to the relevance of super-exchange in both phases. We show that super-exchange is not the main mechanism driving these transitions. Specifically, it is not strong enough to be responsible for the high-temperature cubic to tetragonal transition and does not yield the type of orbital order observed in the monoclinic phase. The energy difference between the tetragonal and the monoclinic structure is tiny, and most likely results from the interplay between volume, covalency, and localization effects. The transition is rather driven by Slater exchange than super-exchange. Nevertheless, once the monoclinic distortions are present, super-exchange helps in stabilizing the low symmetry structure. The orbital order we obtain for this monoclinic phase is consistent with the magnetic transition at 80 K., Comment: 8 pages, 6 figures

Orbital and spin ordering phenomena in strongly correlated systems are commonly studied using the local-density approximation + dynamical mean-field theory approach. Typically, however, such simulations are restricted to simplified models (density-density Coulomb interactions, high symmetry couplings and few-band models). In this work we implement an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) which allows us to investigate orbital and spin ordering in a more realistic setting, including interactions that are often neglected (e.g., spin-flip and pair-hopping terms), enlarged basis sets (full d versus eg), low-symmetry distortions, and reaching the very low-temperature (experimental) regime. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides: LaMnO3 and rare-earth manganites as well as the perovskites CaVO3 and YTiO3. We show that spin-flip and pair hopping terms do not affect the Kugel-Khomskii orbital-order melting transition in rare-earth manganites, or the suppression of orbital fluctuations driven by crystal field and Coulomb repulsion. For the Mott insulator YTiO3 we find a ferromagnetic transition temperature 50 K, in remarkably good agreement with experiments. For LaMnO3 we show that the classical t2g-spin approximation, commonly adopted for studying manganites, yields indeed an occupied eg orbital in very good agreement with that obtained for the full d 5-orbital Hubbard model, while the spin-spin e_g-t_{2g} correlation function calculated from the full d model is 0.74, very close to the value expected for aligned eg and t2g spins; the eg spectral function matrix is also well reproduced. Finally, we show that the t2g screening reduces the eg-eg Coulomb repulsion by about 10%, Comment: 9 pages, 5 figures

Spin-state transitions are the hallmark of rare-earth cobaltates. In order to understand them, it is essential to identify all relevant parameters which shift the energy balance between spin states, and determine their trends. We find that \Delta, the eg-t2g crystal-field splitting, increases by ~250 meV when increasing pressure to 8 GPa and by about 150 meV when cooling from 1000K to 5K. It changes, however, by less than 100 meV when La is substituted with another rare earth. Also the Hund's rule coupling J_avg is about the same in systems with very different spin-state transition temperature, like LaCoO3 and EuCoO3. Consequently, in addition to \Delta and J_avg, the Coulomb-exchange anisotropy \Delta J_ avg and the super-exchange energy-gain \Delta E_SE play a crucial role, and are comparable with spin-state dependent relaxation effects due to covalency. We show that in the LnCoO3 series, with Ln=Y or a rare earth (RE), super-exchange progressively stabilizes a low-spin ground state as the Ln^{3+} ionic radius decreases. We give a simple model to describe spin-state transitions and show that, at low temperature, the formation of isolated high-spin/low-spin pairs is favored, while in the high-temperature phase, the most likely homogeneous state is high-spin, rather than intermediate spin. An orbital-selective Mott state could be a fingerprint of such a state., Comment: 10 pages, 9 figures

We study the mechanism of orbital-order melting observed at temperature T_OO in the series of rare-earth manganites. We find that many-body super-exchange yields a transition-temperature T_KK that decreases with decreasing rare-earth radius, and increases with pressure, opposite to the experimental T_OO. We show that the tetragonal crystal-field splitting reduces T_KK further increasing the discrepancies with experiments. This proves that super-exchange effects, although very efficient, in the light of the experimentally observed trends, play a minor role for the melting of orbital ordering in rare-earth manganites., Comment: 4 pages, 5 figures

We present a general method for determining screened Coulomb parameters in molecular assemblies, in particular organic molecular crystals. This allows us to calculate the interaction parameters used in a generalized Hubbard model description of correlated organic materials. In such a model only the electrons in levels close to the Fermi level are included explicitly, while the effect of all other electrons is included as a renormalization of the model parameters. For the Coulomb integrals this renormalization is mainly due to screening. For molecular materials we can split the screening into intra- and inter-molecular screening. Here we demonstrate how the inter-molecular screening can be calculated by modeling the molecules by distributed point-polarizabilities and solving the resulting self-consistent electrostatic screening problem in real space. For the example of the quasi one-dimensional molecular metal TTF-TCNQ we demonstrate that the method gives remarkably accurate results., Comment: Submitted to Special Issue - ISCOM 2009 - Physica B Condensed Matter

The origin of the cooperative Jahn-Teller distortion and orbital-order in LaMnO3 is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO3-type distortions and the strong Hund's rule coupling between e_g and t_2g electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of super-exchange from those of lattice distortions. We find that super-exchange alone would yield T_KK=650 K. The tetragonal and GdFeO3-type distortions, however, reduce T_KK to 550 K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to at least 1150 K and to reproduce the occupied orbital deduced from neutron scattering., Comment: 4 pages, 3 figures; published version (minor changes)

We analyze cellular dynamical mean-field theory (CDMFT) and the dynamical cluster approximation (DCA). We derive exact sum-rules for the hybridization functions and give examples for DMFT, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum-rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath-parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. In two dimensions we find, that we need so many bath-sites to obtain a reliable parametrization that Lanczos calculations are hardly feasible with current computers. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization., Comment: 11 pages, 14 figures

We employ density-functional theory to calculate realistic parameters for an extended Hubbard model of the molecular metal TTF-TCNQ. Considering both intra- and intermolecular screening in the crystal, we find significant longer-range Coulomb interactions along the molecular stacks, as well as inter-stack coupling. We show that the long-range Coulomb term of the extended Hubbard model leads to a broadening of the spectral density, likely resolving the problems with the interpretation of photoemission experiments using a simple Hubbard model only., Comment: 4 pages, 2 figures

We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within linear response of Kotliar-Ruckenstein slave-bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction U strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover the vertex function does not show particularly strong forward scattering. Going to larger temperatures kT\sim t we find that after an initial decrease with U, the electron-phonon coupling starts to increase with U, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature., Comment: 4 pages, 6 figures

We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down close to the Mott transition. Away from half filling RPA is much less reliable: Already for very small values of the Hubbard interaction U, the linear response becomes much more efficient than RPA, eventually leading to overscreening already beyond quite moderate values of U. To understand this behavior we give a simple argument, which implies that the response to an external perturbation at large U should actually be strongly non-linear. This prediction is confirmed by the results of exact diagonalization., Comment: 10 pages, 7 figures, RevTeX

We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions for interacting systems. In addition we demonstrate that the characterization of metals and insulators by the decay properties of their respective density matrices does not only apply to non-interacting, but also to interacting systems. As a prototypical example of a correlated system we investigate the one-dimensional Hubbard model. We propose an expression for the density matrix of that model, and derive a relation between the decay constant of the density matrix and the gap., Comment: 9 pages with 3 eps figures, to be published in Solid State Communications

We study the Mott transition in Hubbard models with a degenerate band on different 3-dimensional lattices. While for a non-degenerate band only the half-filled system may exhibit a Mott transition, with degeneracy there can be a transition for any integer filling. We analyze the filling dependence of the Mott transition and find that $U_c$ (the Hubbard interaction $U$ at which the transition takes place) decreases away from half-filling. In addition we can change the lattice structure of the model. This allows us to study the influence of frustration on the Mott transition. We find that frustration increases $U_c$, compared to bipartite systems. The results were obtained from fixed-node diffusion Monte Carlo calculations using trial functions which allow us to systematically vary the magnetic character of the system. To gain a qualitative understanding of the results, we have developed simple hopping arguments that help to rationalize the doping dependence and the influence of frustration on the Mott transition. Choosing the model parameters to describe the doped Fullerides, we can make contact with experiment and understand why some of the Fullerides are metals, while others, which according to density functional theory should also be metallic, actually are insulators., Comment: 4 pages LaTeX with 4 eps figures; submitted to Computer Physics Communications, Proceedings of the CPP'99/Centennial Meeting, Atlanta, GA; additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

We use the doped Fullerenes as an example of how realistic systems can be described by simple models. Starting from the band structure we set up a tight-binding model that describes the t_{1u} conduction band. Adding correlation terms we arrive at a generalized Hubbard Hamiltonian that we treat using quantum Monte Carlo. To address the problem of superconductivity in the doped Fullerenes, we study the screening of a point charge. We find surprisingly efficient metallic screening even for strong correlations, almost up to the Mott transition, and discuss the implications on superconductivity, in particular the effect of the efficient screening on the Coulomb pseudopotential and the electron-phonon coupling., Comment: 9 pages LaTeX with 2 eps figures; Proceedings of the International Conference on Statistical Mechanics and Strongly Correlated Electrons in honor of Giovanni Paladin, Sept 27-29, 1999, Universita di Roma "La Sapienza"; additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

Describing the doped Fullerenes using a generalized Hubbard model, we study the Mott transition for different integer fillings of the t_1u band. We use the opening of the energy-gap E_g as a criterion for the transition. E_g is calculated as a function of the on-site Coulomb interaction U using fixed-node diffusion Monte Carlo. We find that for systems with doping away from half-filling the Mott transitions occurs at smaller U than for the half-filled system. We give a simple model for the doping dependence of the Mott transition., Comment: 7 pages RevTeX with 10 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

We study the static screening in a Hubbard-like model using fixed-node diffusion Monte Carlo. We find that the random phase approximation is surprisingly accurate even for metallic systems close to the Mott transition. As a specific application we discuss the implications of the efficient screening for the superconductivity in the doped Fullerenes. In the Monte Carlo calculations we use trial functions with two Gutzwiller-type parameters. To deal with such trial functions, we introduce a method for efficiently optimizing the Gutzwiller parameters, both in variational and in fixed-node diffusion Monte Carlo., Comment: 4 pages LaTeX with 4 eps figures; Computer Simulations Studies in Condensed Matter Physics XII, Eds.: D.P. Landau, S.P. Lewis, and H.B. Schuettler, Springer 1999; additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

Gutzwiller functions are popular variational wavefunctions for correlated electrons in Hubbard models. Following the variational principle, we are interested in the Gutzwiller parameters that minimize e.g. the expectation value of the energy. Rewriting the expectation value as a rational function in the Gutzwiller parameters, we find a very efficient way for performing that minimization. The method can be used to optimize general Gutzwiller-type wavefunctions both, in variational and in fixed-node diffusion Monte Carlo., Comment: 9 pages RevTeX with 10 eps figures

We study the static screening in a Hubbard-like model using quantum Monte Carlo. We find that the random phase approximation is surprisingly accurate almost up to the Mott transition. We argue that in alkali-doped Fullerenes the Coulomb pseudopotential $\mu^\ast$ is not very much reduced by retardation effects. Therefore efficient screening is important in reducing $\mu^{\ast}$ sufficiently to allow for an electron-phonon driven superconductivity. In this way the Fullerides differ from the conventional picture, where retardation effects play a major role in reducing the electron-electron repulsion., Comment: 4 pages RevTeX with 2 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

Fullerides are crystals made from C60 molecules. When doped with alkali metals the valence electrons of the alkali atoms are transfered to the C60 molecules. We show how to set up a model Hamiltonian to describe the correlated hopping of these electrons between C60 molecules. Then we discuss Monte Carlo methods for such lattice Hamiltonians, putting special emphasis on the optimization of Gutzwiller wavefunctions both in variational and fixed-node diffusion Monte Carlo. As application of these methods we analyze the metal-insulator transition in the integer-doped Fullerides., Comment: 16 pages, 10 eps figures included; Proceedings of the NATO ASI Quantum Monte Carlo Methods in Physics and Chemistry, Cornell University, July, 12-25, 1998; additional information is available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

For conventional superconductors the electron-electron interaction is strongly reduced by retardation effects, making the formation of Cooper pairs possible. In the alkali-doped Fullerides, however, there are no strong retardation effects. But dielectric screening can reduce the electron-electron interaction sufficiently, if we assume that the random-phase approximation (RPA) is valid. It is not clear, however, if this assumption holds, since the alkali-doped Fullerides are strongly correlated systems close to a Mott transition. To test the validity of the RPA for these systems we have calculated the screening of a test charge using quantum Monte Carlo., Comment: 4 pages, 1 eps figure included; to be published in the proceedings of the International Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, 1998; additional information is available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

The doped Fullerides can be well described by a Hubbard model, which comprises the partly filled, threefold-degenerate t_1u orbital and the on-site Coulomb interaction U. The orbital degeneracy is known to shift the critical ratio U_c/W for the Mott-Hubbard transition towards larger values. This puts the half-filled alkali-doped Fullerides A_3 C_60 on the metallic side of the transition. Prompted by the recent synthesis of isostructural families of integer-doped Fullerides with different fillings, we investigate how the orbital degeneracy affects the Mott transition at integer fillings different from 3. The calculations are done by fixed-node diffusion Monte Carlo, using a trial function, which permits us to systematically vary the magnetic character of the system., Comment: 4 pages LaTeX, 2 eps figures included; additional information available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

We study how the electron hopping reduces the Mott-Hubbard band gap in the limit of a large Coulomb interaction U and as a function of the orbital degeneracy N. The results support the conclusion that the hopping contribution grows as roughly \sqrt{N}W, where W is the one-particle band width, but in certain models a crossover to a \sim NW behavior is found for a sufficiently large N., Comment: 7 pages, revtex, 6 figures more information at http://www.mpi-stuttgart.mpg.de/dokumente/andersen/fullerene/