Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo

TL;DR

This paper introduces a novel approach that combines dynamic mean-field theory with diagrammatic Monte Carlo to significantly improve convergence and efficiency in calculating properties of lattice models, demonstrated on Anderson localization.

Contribution

The paper presents a new method integrating DMFT into BDMC, enhancing unbiased sampling efficiency for lattice models in non-perturbative regimes.

Findings

Achieved a 10,000-fold improvement in convergence over traditional BDMC.

Successfully computed the density of states in the Anderson localization regime.

Demonstrated the method's power in non-perturbative lattice model analysis.

Abstract

The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feynman's diagrammatic series using skeleton diagrams. For lattice models the efficiency of BDMC can be dramatically improved by incorporating dynamic mean-field theory (DMFT) solutions into renormalized propagators. From the DMFT perspective, combining it with BDCM leads to an unbiased method with well-defined 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 localization problem, where a gain of the order of $10^4$ is achieved with respect to conventional BDMC in terms of convergence to the exact answer.