Diagrammatic Monte Carlo

Abstract

Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. Starting with a general introduction to the principles of DiagMC, we present a detailed description of the DiagMC scheme for interacting fermions (Hubbard model), as well as the first illustrative results for the equations of state.

15 pages, 7 figures. To appear in: Computer Simulation Studies in Condensed Matter Physics XXI, Eds. D.P. Landau, S.P. Lewis, and H.B. Schuttler (Springer Verlag, Heidelberg, Berlin 2008)

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• Quantum Cluster Theories
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Diagrammatic Quantum Monte Carlo for Two-Body Problem: Exciton
• Bold diagrammatic Monte Carlo: A generic technique for polaron (and many-body?) problems

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