Efficiency of quantum Monte Carlo impurity solvers for dynamical mean-field theory

Since the inception of the dynamical mean-field theory, numerous numerical studies have relied on the Hirsch-Fye quantum Monte Carlo (HF-QMC) method for solving the associated impurity problem. Recently developed continuous-time algorithms (CT-QMC) avoid the Trotter discretization error and allow for faster configuration updates, which makes them candidates for replacing HF-QMC. We demonstrate, however, that a state-of-the-art implementation of HF-QMC (with extrapolation of discretization delta_tau -> 0) is competitive with CT-QMC. A quantitative analysis of Trotter errors in HF-QMC estimates and of appropriate delta_tau values is included.Comment: 6 pages, 9 figures; minor changes; version accepted for PR

The Mott insulator - 10th order perturbation theory extended to infinite order using QMC

We present a new method, based on the combination of analytical and numerical techniques within the framework of the dynamical mean-field theory (DMFT). Building upon numerically exact results obtained in an improved quantum Monte Carlo (QMC) scheme, 10th order strong-coupling perturbation theory for the Hubbard model on the Bethe lattice is extrapolated to infinite order. We obtain continuous estimates of energy E and double occupancy D with unprecedented precision O(10^{-5}) for the Mott insulator above its stability edge U_{c1}=4.78 as well as critical exponents. The relevance for recent experiments on Cr-doped V_2O_3 is pointed out.Comment: 4 pages, 5 figures. Significant changes in introduction and summary; experimental reference added; Figs. 1 and 3 modifie

Ground state of the frustrated Hubbard model within DMFT: energetics of Mott insulator and metal from ePT and QMC

We present a new method, ePT, for extrapolating few known coefficients of a perturbative expansion. Controlled by comparisons with numerically exact quantum Monte Carlo (QMC) results, 10th order strong-coupling perturbation theory (PT) for the Hubbard model on the Bethe lattice is reliably extrapolated to infinite order. Within dynamical mean-field theory (DMFT), we obtain continuous estimates of energy E and double occupancy D with unprecedented precision O(10^{-5}) for the Mott insulator above its stability edge U_{c1}=4.78 as well as critical exponents. In addition, we derive corresponding precise estimates for E and D in the metallic ground state from extensive low-temperature QMC simulations using a fit to weak-coupling PT while enforcing thermodynamic consistency.Comment: 2 pages, 5 figures, submitted to SCES '0

Superconductivity of SrTiO_{3-\delta}

Superconducting SrTiO_{3-\delta} was obtained by annealing single crystalline SrTiO_3 samples in ultra high vacuum. An analysis of the V(I) characteristics revealed very small critical currents I_c which can be traced back to a unavoidable doping inhomogeneity. R(T) curves were measured for a range of magnetic fields B at I<<I_c, thereby probing only the sample regions with the highest doping level. The resulting curves B_{c2}(T) show upward curvature, both at small and strong doping. These results are discussed in the context of bipolaronic and conventional superconductivity with Fermi surface anisotropy. We conclude that the special superconducting properties of SrTiO_{3-\delta} can be related to its Fermi surface and compare this finding with properties of the recently discovered superconductor MgB_2.Comment: EPJ style, 6 pages, 8 figures; minor changes, Fig. 5 replaced; use PDF version for printout