J. Phys. IV France 10 (2000) Pr5-3-Pr5-16
Path integral Monte Carlo simulations for fermion systems : Pairing in the electron-hole plasmaJ. Shumway and D. M. Ceperley
National Center for Supercomputing Applications and Department of Physics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, U.S.A.
We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to possible "cross-linking" of polymers. As proposed by Feynman, superfluidity and Bose condensation result from macroscopic exchange of bosons. To map fermions onto a positive probability distribution, one must restrict the paths to lie in regions where the fermion density matrix is positive. We discuss a recent application to the two-component electron-hole plasma. At low temperature excitons and bi-excitons form. We have used nodal surfaces incorporating paired fermions and see evidence of a Bose condensation in the energy, specific heat and superfluid density. In the restricted path integral picture, pairing appears as intertwined electron-hole paths. Bose condensation occurs when these intertwined paths wind around the periodic boundaries.
© EDP Sciences 2000