Quantum Monte Carlo simulations of exciton condensates

We have studied scattering states and thermodynamic properties of electron–hole systems. Starting from the constituent electrons and holes and Coulomb interactions, we have used quantum Monte Carlo simulation techniques to sample properties of wavefunctions and thermal density matrices. We have studied three types of systems: (1) the scattering of two excitons, with full-quantum treatment of the four constituent particles, (2) the thermodynamic equilibrium of 14 electron–hole pairs having two spin states for each particle, which form excitons and biexcitons at low temperatures, and (3) the thermodynamic equilibrium of 27 spin-polarized electron–hole pairs, which form a dilute exciton gas that undergoes Bose condensation at low temperatures. We compare our results with predictions of the Saha equation for exciton and biexciton formation, and Bogoliubov theory for the energy of the dilute Bose gas of excitons. We also discuss the outlook for future quantum Monte Carlo simulations on these systems.