Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo

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.

4 pages, 3 figures

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• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm
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• Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron
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• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Feasibility of Diagrammatic Monte-Carlo based on weak-coupling expansion in asymptotically free theories: case study of $O(N)$ sigma-model in the large-$N$ limit