67 research outputs found

### 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

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