Berlin 2008 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 23: Correlated Electrons: (General) Theory

TT 23.1: Talk

Wednesday, February 27, 2008, 14:00–14:15, H 0104

Multigrid Hirsch-Fye quantum Monte Carlo solver for dynamical mean-field theory — •Nils Blümer — Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz

The dynamical mean-field theory (DMFT) is a nonperturbative approach to Hubbard-type models in which an impurity model has to be solved self-consistently. This is possible nonperturbatively using the Hirsch-Fye quantum Monte-Carlo (HF-QMC) algorithm which introduces an imaginary-time discretization Δτ. The associated Trotter error impacts all "raw" HF-QMC results including phase boundaries, Green functions, spectra, and scalar observables such as energies and quasiparticle weights. Unbiased estimates of scalar observables can be derived from HF-QMC data by extrapolation Δτ→ 0, with high precision and efficiency [1]. However, this a posteriori correction of the Trotter error is problematic close to phase boundaries and could so far not be applied to Green functions and spectra.

In this talk, I show how numerically exact Green functions can be extrapolated from HF-QMC estimates and construct a multigrid HF-QMC algorithm which eliminates the discretization error within the DMFT self-consistency cycle. In contrast to conventional HF-QMC, the multigrid algorithm converges to the numerically exact fixed point(s) and allows for the direct determination of phase boundaries without further extrapolation. It extends the useful range of Δτ values and yields unbiased estimates of observables with high precision and efficiency, even close to phase transitions.

[1] N. Blümer, to appear in Phys. Rev. B [arXiv:0708.1749v3].