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 defined on discretized space-time 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 lattice field theory aproach for electrons in a

semiconductor nanoparticle may have 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, and to

a 1.8 nm hetero-structured (Janus-type) NC Cd₃₇Pb₃₁Se₆₈ with 1582 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 G₀W₀ calculations. This formalism naturally allows

calculations of more complex excited states, such as excitons and trions, for which we present some results.