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. This is due to the oscillatory nature of the integrand exp (−S ), where S is the imaginary-time action. This issue is a major obstacle to first-principles lattice quantum Monte Carlo studies of excited states of electrons in matter. 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 in the functional integral, 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.