Carey Huscroft

Quantum Monte Carlo algorithm for nonlocal 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.

Signatures of spin and charge energy scales in the local moment and specific heat of the half-filled two-dimensional Hubbard model

Local moment formation driven by the on-site repulsion U is one of the most fundamental features in the Hubbard model. At the simplest level, the temperature dependence of the local moment is expected to have a single structure at T{approx}U, reflecting the suppression of the double occupancy. In this paper we show low-temperature quantum Monte Carlo data for half-filling which emphasize that the local moment also has a signature at a lower energy scale which previously had been thought to characterize only the temperatures below which moments on different sites begin to correlate locally. We discuss implications of these results for the structure of the specific heat, and connections to quasiparticle resonance and pseudogap formation in the density of states.

Maximum entropy method of obtaining thermodynamic properties from quantum Monte Carlo simulations

We describe a method of obtaining thermodynamic properties of quantum systems using Bayesian 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 nontrivial example of the method, we obtain the specific heat of the three-dimensional periodic Anderson model.

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 Hartee-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 volumecollapse phenomenon experimentally observed in f-electron systems.

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 Gutzwillers variational method and the Hubbard-III approximation (which corresponds to an exact solution of the appropriate Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value

Local moment and specific heat in the Hubbard model

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The Dynamical Cluster Approximation: A New Technique for Simulations of Strongly Correlated Electron Systems

of the hybridization (or above a critical interaction

Method of reducing power consumption of a computing system by evacuating selective platform memory components thereof

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Server configured for managing power and performance

the system is an insulator in Gutzwillers and a semimetal in Hubbards approach, whereas above

Pseudogaps in the 2D Hubbard Model

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