Diagrammatic Monte Carlo

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In mathematical physics, the diagrammatic Monte Carlo method is based on stochastic summation of Feynman diagrams with controllable error bars. [1] [2] It was developed by Boris Svistunov and Nikolay Prokof'ev. It was proposed as a generic approach to overcome the numerical sign problem that precludes simulations of many-body fermionic problems. [3] Diagrammatic Monte Carlo works in the thermodynamic limit, and its computational complexity does not scale exponentially with system or cluster volume. [4]

References

  1. ↑ Van Houcke, K.; Werner, F.; Kozik, E.; Prokof’ev, N.; Svistunov, B.; Ku, M. J. H.; Sommer, A. T.; Cheuk, L. W.; Schirotzek, A. (2012-03-18). "Feynman diagrams versus Fermi-gas Feynman emulator". Nature Physics. 8 (5): 366–370. arXiv: 1110.3747 . doi:10.1038/nphys2273. ISSN   1745-2473. S2CID   53412117.
  2. ↑ Prokof’ev, Nikolay; Svistunov, Boris (2007-12-18). "Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome". Physical Review Letters. 99 (25): 250201. arXiv: cond-mat/0702555 . doi:10.1103/PhysRevLett.99.250201. PMID   18233498. S2CID   42616665.
  3. ↑ Rossi, R.; Prokof'ev, N.; Svistunov, B.; Van Houcke, K.; Werner, F. (2017-04-01). "Polynomial complexity despite the fermionic sign". EPL (Europhysics Letters). 118 (1): 10004. arXiv: 1703.10141 . doi:10.1209/0295-5075/118/10004. ISSN   0295-5075. S2CID   17929942.
  4. ↑ Houcke, Kris Van; Kozik, Evgeny; Prokof'ev, N.; Svistunov, B. (2010). "Diagrammatic Monte Carlo". Physics Procedia. 6: 95–105. arXiv: 0802.2923 . doi:10.1016/j.phpro.2010.09.034. hdl: 1854/LU-3234513 . ISSN   1875-3892. S2CID   16490610.


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