Path Integral Monte Carlo Simulations for Fermion Systems: Pairing in the Electron-Hole Plasma

TL;DR

This paper reviews the path integral Monte Carlo method for simulating fermion systems, specifically applying it to an electron-hole plasma to observe pairing and Bose condensation phenomena.

Contribution

It introduces a novel application of the restricted path integral Monte Carlo method to fermion systems, demonstrating pairing and Bose condensation in an electron-hole plasma.

Findings

Evidence of pairing in electron-hole paths

Observation of Bose condensation through winding paths

Identification of superfluidity indicators in energy and specific heat

Abstract

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.