A Maximum Entropy Method of Obtaining Thermodynamic Properties from Quantum Monte Carlo Simulations

We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte Carlo Simulations. The internal energy and the specific heat of the system are easily obtained as are errorbars on these quantities. The entropy and the free energy are also obtainable. No assumptions as to the specific functional form of the energy are made. The use of a priori information, such as a sum rule on the entropy, is built into the method. As a non-trivial example of the method, we obtain the specific heat of the three-dimensional Periodic Anderson Model.Comment: 8 pages, 3 figure

Nanometer Scale Mapping of the Density of States in an Inhomogeneous Superconductor

Using high speed scanning tunneling spectroscopy, we perform a full mapping of the quasiparticle density of states (DOS) in single crystals of BiPbSrCaCuO(2212). The measurements carried out at 5 K showed a complex spatial pattern of important variations of the local DOS on the nanometer scale. Superconducting areas are co-existing with regions of a smooth and larger gap-like DOS structure. The superconducting regions are found to have a minimum size of about 3 nm. The role of Pb-introduced substitutional disorder in the observed spatial variations of the local DOS is discussed.Comment: 4 page Letter with 3 figures (2 color figures

Quantum critical point in a periodic Anderson model

We investigate the symmetric Periodic Anderson Model (PAM) on a three-dimensional cubic lattice with nearest-neighbor hopping and hybridization matrix elements. Using Gutzwiller's variational method and the Hubbard-III approximation (which corresponds to the exact solution of an appropriate Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value $V_c$ of the hybridization (or above a critical interaction $U_c$) the system is an {\em insulator} in Gutzwiller's and a {\em semi-metal} in Hubbard's approach, whereas above $V_c$ (below $U_c$) it behaves like a metal in both approximations. These predictions are compared with the density of states of the $d$- and $f$-bands calculated from Quantum Monte Carlo and NRG calculations. Our conclusion is that the half-filled symmetric PAM contains a {\em metal-semimetal transition}, not a metal-insulator transition as has been suggested previously.Comment: ReVteX, 10 pages, 2 EPS figures. Minor corrections made in the text and in the figure captions from the first version. More references added. Accepted for publication in Physical Review

Depleted Kondo Lattices

We consider a two dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field quantum Monte Carlo methods without sign problems. To achieve the relevant energy scales on finite clusters, we introduce a simple method to reduce size effects by up to an order of magnitude in temperature. In this model, a metallic phase survives up to arbitrarily low temperatures before being disrupted by magnetic fluctuations which open a gap in the charge sector. We study the formation of the heavy-electron state with emphasis on a crossover scale T* defined by the maximum in the resistivity versus temperature curve. The behavior of thermodynamic properties such as specific heat as well as spin and charge uniform susceptibilities are studied as the temperature varies in a wide range across T*. Within our accuracy T* compares well to the Kondo scale of the related single impurity problem. Finally our QMC resuls are compared with mean-field approximations.Comment: 12 pages, 13 figures. Submitted to Phys. Rev.

Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures

The single band Hubbard and the two band Periodic Anderson Hamiltonians have traditionally been applied to rather different physical problems - the Mott transition and itinerant magnetism, and Kondo singlet formation and scattering off localized magnetic states, respectively. In this paper, we compare the magnetic and charge correlations, and spectral functions, of the two systems. We show quantitatively that they exhibit remarkably similar behavior, including a nearly identical topology of the finite temperature phase diagrams at half-filling. We address potential implications of this for theories of the rare earth ``volume collapse'' transition.Comment: 4 pages (RevTeX) including 4 figures in 7 eps files; as to appear in Phys. Rev. Let

A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation

We present the algorithmic details of the dynamical cluster approximation (DCA), with a quantum Monte Carlo (QMC) method used to solve the effective cluster problem. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA) while preserving the lattice symmetries. The DCA becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. We present a generalization of the Hirsch-Fye QMC algorithm for the solution of the embedded cluster problem. We use the two-dimensional Hubbard model to illustrate the performance of the DCA technique. At half-filling, we show that the DCA drives the spurious finite-temperature antiferromagnetic transition found in the DMFA slowly towards zero temperature as the cluster size increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that there is a finite temperature metal to insulator transition which persists into the weak-coupling regime. This suggests that the magnetism of the model is Heisenberg like for all non-zero interactions. Away from half-filling, we find that the sign problem that arises in QMC simulations is significantly less severe in the context of DCA. Hence, we were able to obtain good statistics for small clusters. For these clusters, the DCA results show evidence of non-Fermi liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure

Doping-dependent study of the periodic Anderson model in three dimensions

We study a simple model for $f$-electron systems, the three-dimensional periodic Anderson model, in which localized $f$ states hybridize with neighboring $d$ states. The $f$ states have a strong on-site repulsion which suppresses the double occupancy and can lead to the formation of a Mott-Hubbard insulator. When the hybridization between the $f$ and $d$ states increases, the effects of these strong electron correlations gradually diminish, giving rise to interesting phenomena on the way. We use the exact quantum Monte-Carlo, approximate diagrammatic fluctuation-exchange approximation, and mean-field Hartree-Fock methods to calculate the local moment, entropy, antiferromagnetic structure factor, singlet-correlator, and internal energy as a function of the $f-d$ hybridization for various dopings. Finally, we discuss the relevance of this work to the volume-collapse phenomenon experimentally observed in f-electron systems.Comment: 12 pages, 8 figure