Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

The fermion sign problem, when severe, prevents the computation of physical quantities of a system of interacting fermions via stochastic evaluation of its path integral due to the oscillatory nature of the integrand exp(-S), where S is the imaginary-time action. However, in the Kohn-Sham orbital basis, which is the output of a Density Functional Theory simulation, the path integral for electrons in a semiconductor nanoparticle has only a mild fermion sign problem and is amenable to evaluation by standard stochastic methods. This is evidenced by our simulations of silicon hydrogen-passivated nanocrystals, such as Si35H36, Si87H76, Si147H100 and Si293H172, which range in size 1.0 - 2.4 nm and contain 176 to 1344 valence electrons. We find that approximating the fermion action by its leading order polarization term results in a positive-definite integrand, and is a very good approximation of the full action. We compute imaginary-time electron propagators and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of previous high-precision G0W0 calculations. This formalism allows calculations of more complex excited states, such as excitons and trions.