- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods

K. Mikelsons*

A. Macridin

M. Jarrell

  • Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA

  • Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA

  • Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA

  • *mikelsk@email.uc.edu
PDF

Phys. Rev. E 79, 057701 – Published 13 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.057701

Abstract

Two weak-coupling continuous time quantum Monte Carlo (CTQMC) methods are shown to be equivalent for Hubbard-type interactions. A relation between these CTQMC methods and the Hirsch-Fye quantum Monte Carlo (HFQMC) method is established, identifying the latter as an approximation within CTQMC and providing a diagrammatic interpretation. Both HFQMC and CTQMC are shown to be equivalent when the number of time slices in HFQMC becomes infinite, implying the same degree of fermion sign problem in this limit.

View figure in article

Article Text

References (12)

  1. J. E. Hirsch and R. M. Fye, Phys. Rev. Lett. 56, 2521 (1986).
  2. R. M. Fye and J. E. Hirsch, Phys. Rev. B 38, 433 (1988).
  3. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
  4. F. F. Assaad, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, NIC Series Vol. 10 edited by J. Grotendorst, D. Marx, and A. Muramatsu (John von Neumann Institute for Computing, Jülich, 2002), pp. 99–156.
  5. R. R. dos Santos, Braz. J. Phys. 33, 36 (2003).
  6. N. V. Prokof’ev, B. V. Svistunov, and I. S. Tupitsyn, JETP Lett. 64, 911 (1996).
  7. S. M. A. Rombouts, K. Heyde, and N. Jachowicz, Phys. Rev. Lett. 82, 4155 (1999).
  8. A. N. Rubtsov, V. V. Savkin, and A. I. Lichtenstein, Phys. Rev. B 72, 035122 (2005).
  9. J. Hubbard, Proc. R. Soc. London, Ser. A 276, 238 (1963); M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963); J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).
  10. E. Gull, P. Werner, O. Parcollet, and M. Troyer, Europhys. Lett. 82, 57003 (2008).
  11. F. F. Assaad and T. C. Lang, Phys. Rev. B 76, 035116 (2007).
  12. J. E. Hirsch, Phys. Rev. B 28, 4059 (1983).

Outline

Information

Phys. Rev. E 79, 057701– Published 13 May, 2009
  • Received 18 August 2008

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation