Advertisement

Dynamics and Criticality of Correlated Electrons and Quantum Gases

  • C. Lavalle
  • M. Rigol
  • J. Hub
  • A. Muramatsu
Conference paper

Abstract

Quantum Monte Carlo simulations are used to study the dynamics and the critical properties of strongly correlated systems relevant to the fields of cold quantum gasses and high-T c superconductivity. Recent advances in cooling techniques of quantum gasses allow to reach the degenerate regime for fermionic samples. Loading these systems on optical lattices can bring the gas to a strongly correlated regime. We analyze the properties of trapped degenerate Fermi gasses on optical lattices and show that they display quantum critical behavior and universality at the boundaries between metallic and Mott insulating phases. On our other field of interest, high-T c superconductivity, a Quantum Monte Carlo algorithm we developed recently is used to study the dynamics of the nearest-neighbor (n.n) t-J model relevant to the low energy properties of the copper oxides materials. We show that antiholons identified in the supersymmetric inverse squared (ISE) t-J model are generic excitation of the n.n. model since they are clearly visible in the single-particle spectral function of the n.n. t-J model in the whole Luttinger-liquid regime. We have further shown that even the analysis of the two-particle spectral functions of the n.n. t-J model can be based on the elementary excitations of the ISE t-J model.

Keywords

Optical Lattice Spinless Fermion Quantum Monte Carlo Simulation Charge Velocity Charge Correlation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [GREI02]
    M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, Nature (London) 415, 39 (2002).CrossRefGoogle Scholar
  2. [OHAR02]
    K.M. O’Hara, S.L. Hemmer, M.E. Gehm, S.R. Granade, and J.E. Thomas, Science 298, 2179 (2002).CrossRefGoogle Scholar
  3. [RIGO03]
    M. Rigol, A. Muramatsu, G.G. Batrouni, and R.T. Scalettar, Phys. Rev. Lett. 91, 130403 (2003).CrossRefGoogle Scholar
  4. [RIGO04]
    M. Rigol and A. Muramatsu, Phys. Rev. A 69, 053612 (2004).CrossRefGoogle Scholar
  5. [BATR02]
    G.G. Batrouni, V. Rousseau, R.T. Scalettar, M. Rigol, A. Muramatsu, P.J.H. Denteneer, and M. Troyer, Phys. Rev. Lett. 89, 117203 (2002).CrossRefGoogle Scholar
  6. [MURA99]
    A. Muramatsu, in Quantum Monte Carlo Methods in Physics and Chemistry, edited by M.P. Nightingale and C.J. Umrigar (NATO Science Series, Kluwer Academic Press, Dordrecht, 1999), pp. 343–373.Google Scholar
  7. [LIEB68]
    E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).CrossRefGoogle Scholar
  8. [SCHA91]
    A. Schadschneider and J. Zittartz, Z. Phys. B 82, 387 (1991).CrossRefMathSciNetGoogle Scholar
  9. [BEDN86]
    G.J. Bednorz and K.A. Müller, Z. Phys. B 64, 188 (1986)CrossRefGoogle Scholar
  10. [ASSA91]
    M. Ogata, M.U. Luchini, S. Sorella and F. Assaad, Phys. Rev. Lett. 66, 2388 (1991)CrossRefGoogle Scholar
  11. [NAKA97]
    M. Nakamura, K. Nomura and A. Kitazawa, Phys. Rev. Lett. 79, 3214 (1997)CrossRefGoogle Scholar
  12. [SUGI86]
    G. Sugiyama and S.E. Koonin, Anals of Phys. 168, 1 (1986).CrossRefGoogle Scholar
  13. [BLAN81]
    R. Blankenbecler, R.L. Sugar, and D.J. Scalapino, Phys. Rev. D 24, 2278 (1981).CrossRefGoogle Scholar
  14. [BEMM94]
    H.J.M. van Bemmel, D.F.B. ten Haaf, W. van Saarlos, J.M.J. van Leeuwen and G. An, Phys. Rev. Lett. 72, 2442 (1994).CrossRefGoogle Scholar
  15. [HAAF95]
    D.F.B. ten Haaf, H.J.M. van Bemmel, J.M.J. van Leeuwen, W. van Saarloos and D.M. Ceperley Phys. Rev. B 51, 13039 (1995).CrossRefGoogle Scholar
  16. [SORE99]
    S. Sorella and L. Capriotti, Phys. Rev. B. 61, 2599 (1999).CrossRefGoogle Scholar
  17. [BRUN02]
    M. Brunner, C. Lavalle, F.F. Assaad and A. Muramatsu, Comp. Phys. Comm. 147, 690 (2002).MATHCrossRefGoogle Scholar
  18. [LAVA04]
    C. Lavalle, M. Arikawa and A. Muramatsu, in preparation.Google Scholar
  19. [KHAL90]
    G. Khaliullin, JETP Lett. 52, 389 (1990).Google Scholar
  20. [EVER03]
    H.G. Evertz, Adv. Phys. 52, 1 (2003).CrossRefGoogle Scholar
  21. [LAVA03]
    C. Lavalle, M. Arikawa, S. Capponi, F. Assaad, and A. Muramatsu, Phys. Rev. Lett. 90, 216401 (2003).CrossRefGoogle Scholar
  22. [JARR96]
    M. Jarrell and J. Gubernatis, Phys. Rep. 269, 133 (1996).CrossRefMathSciNetGoogle Scholar
  23. [HAHA94]
    Z.N.C. Ha and F.D.M. Haldane, Phys. Rev. Lett. 73, 2887 (1994).CrossRefGoogle Scholar
  24. [ARIK99]
    M. Arikawa, T. Yamamoto, Y. Saiga and Y. Kuramoto, J. Phys. Soc. Jap. 68, 3782 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • C. Lavalle
    • 1
  • M. Rigol
    • 1
  • J. Hub
    • 1
  • A. Muramatsu
    • 1
  1. 1.Institut für Theoretische Physik IIIUniversität StuttgartStuttgartGermany

Personalised recommendations