Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome

Details Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome

2007-02-23

arxiv.org/abs/cond-mat/0702555v3

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures, revtex4

Scientific paper

10.1103/PhysRevLett.99.250201

We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that of a simple iterative scheme for solving integral equations. With BMC technique, a moderate "sign problem" turns out to be an advantage in terms of the convergence of the process. For an illustrative example, we solve one-particle s-scattering problem. As an important application, we obtain T-matrix for a fermipolaron (one spin-down particle interacting with the spin-up fermionic sea).

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