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 theta(10(-5)) for the Mott insulator above its stability edge U-cl approximate to 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. (c) 2005 Elsevier B.V. All rights reserved.