Time-dependent stochastic Bethe-Salpeter approach

Eran Rabani, Roi Baer, and Daniel Neuhauser
Phys. Rev. B 91, 235302 – Published 1 June 2015

Abstract

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and the configuration-interaction with single substitution (CIS) method. This results in a time-dependent Schrödinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the random-phase approximation (RPA). To solve for the optical-absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of 3000 electrons is presented and discussed.

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  • Received 10 February 2015
  • Revised 25 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235302

©2015 American Physical Society

Authors & Affiliations

Eran Rabani

  • Department of Chemistry, University of California and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Roi Baer

  • Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Daniel Neuhauser

  • Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA

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Issue

Vol. 91, Iss. 23 — 15 June 2015

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