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.Received 29 May 2020Revised 19 August 2020Accepted 3 May 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023173Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structureFirst-principles calculationsNanocrystalsPhysical SystemsSemiconductor compoundsTechniquesDensity functional calculationsCondensed Matter & Materials Physics