Absence of a Slater Transition in The Two-Dimensional Hubbard Model

We present well-controlled results on the metal to insulator transition (MIT) within the paramagnetic solution of the dynamical cluster approximation (DCA) in the two-dimensional Hubbard model at half-filling. In the strong coupling regime, a local picture describes the properties of the model; there is a large charge gap $\Delta \approx U$. In the weak-coupling regime, we find a symbiosis of short-range antiferromagnetic correlations and moment formation cause a gap to open at finite temperature as in one dimension. Hence, this excludes the mechanism of the MIT proposed by Slater long ago.Comment: 4 pages, 5 figure

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

A novel FLEX supplemented QMC approach to the Hubbard model

This paper introduces a novel ansatz-based technique for solution of the Hubbard model over two length scales. Short range correlations are treated exactly using a dynamical cluster approximation QMC simulation, while longer-length-scale physics requiring larger cluster sizes is incorporated through the introduction of the fluctuation exchange (FLEX) approximation. The properties of the resulting hybrid scheme are examined, and the description of local moment formation is compared to exact results in 1D. The effects of electron-electron coupling and electron doping on the shape of the Fermi-surface are demonstrated in 2D. Causality is examined in both 1D and 2D. We find that the scheme is successful if QMC clusters of $N_C\ge 4$ are used (with sufficiently high temperatures in 1D), however very small QMC clusters of $N_C=1$ lead to acausal results

Effect of long-range hopping on Tc in a two-dimensional Hubbard-Holstein model of the cuprates

We study the effect of long-range hoppings on Tc for the two-dimensional (2D) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, t' and t'', generally suppress Tc. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite t' enhances Tc in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.Comment: 5 pages, 4 figure

Transport Properties of the Infinite Dimensional Hubbard Model

Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half filling we observe a gradual crossover from a normal Fermi-liquid with a Drude peak at $\omega=0$ in the optical conductivity to an insulator as a function of $U$ for temperatures above the antiferromagnetic phase transition. When doped, the ``insulator'' becomes a Fermi-liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a $T^2$-coefficient in the low temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.Comment: 14 page

The isotope effect in the Hubbard model with local phonons

The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping whereas the AF susceptibility at intermediate doping increases with decreasing phonon frequency $\omega_0$. This IE stems from increased polaronic effects with decreasing $\omega_0$. A larger IE at smaller doping occurs due to stronger polaronic effects determined by the interplay of the EP interaction with stronger AF correlations. The IE of the Hubbard-Holstein model exhibits many similarities with the IE measured in cuprate superconductors