Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo

L Pollet
Nikolai Prokof'ev, University of Massachusetts - Amherst
Boris Svistunov, University of Massachusetts - Amherst

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Abstract

The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feyn- man's diagrammatic series using skeleton diagrams. For lattice models the eciency of BDMC can be dramatically improved by incorporating dynamic mean-eld theory solutions into renormalized propagators. From the DMFT perspective, combining it with BDCM leads to an unbiased method with well-dened accuracy. We illustrate the power of this approach by computing the single-particle propagator (and thus the density of states) in the non-perturbative regime of the Anderson local- ization problem, where a gain of the order of 104 is achieved with respect to conventional BDMC in terms of convergence to the exact answer.