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arXiv:1805.10554 · Physical review. B./Physical review. B

Swift G W beyond 10,000 electrons using sparse stochastic compression

Vojtěch Vlček, Wenfei Li, Roi Baer, Eran Rabani, Daniel Neuhauser

Published Aug 6, 2018• 76 citations
arXivHTMLPDF

Abstract

We introduce the concept of sparse stochastic compression, an efficient stochastic sampling of any general function. The technique uses sparse stochastic orbitals (SSOs), short vectors that sample a small number of space points. As a first demonstration, SSOs are applied in conjunction with simple direct projection to accelerate our recent stochastic $GW$ technique; the new developments enable accurate prediction of ${G}_{0}{W}_{0}$ quasiparticle energies and gaps for systems with up to ${N}_{e}>10,000$ electrons, with small statistical errors of $\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and using less than 2000 core CPU hours. Overall, stochastic $GW$ scales now linearly (and often sublinearly) with ${N}_{e}.$

DOI
10.1103/physrevb.98.075107

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Stochastic vertex corrections: GWΓXGW\Gamma_XGWΓX​ approach for accurate quasiparticle energies
Quasiparticle energies for the highest occupied and lowest unoccupied states are investigated using the stochastic many-body perturbation theory with the inclusion of non-local vertex corrections. Approximate form of a vertex function, labeled G0W0tcΓXG_0W_0^{tc}\Gamma_XG0​W0tc​ΓX​, is developed and implemented within a real-time stochastic framework. This implementation is tested on acene molecules, C60_{60}60​ and PC60_{60}60​BM. G0W0tcΓXG_0W_0^{tc}\Gamma_XG0​W0tc​ΓX​ is compared to the one-shot stochastic GWGWGW approach with and without random-phase approximation. Overall, the G0W0tcΓXG_0W_0^{tc}\Gamma_XG0​W0tc​ΓX​ method has the best agreement with CCSD(T) benchmark data. The vertex correction appears crucial for the description of unoccupied states. All three stochastic methods scale linearly; due to favorable self-averaging in large systems, stochastic G0W0tcΓXG_0W_0^{tc}\Gamma_XG0​W0tc​ΓX​ is actually less expensive than stochastic G0W0G_0W_0G0​W0​.
We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.
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This thesis develops stochastic many-body methodologies for the electronic structure description of chemically relevant systems with strong electron correlation and nonequilibrium dynamics. Many phenomena of interest in chemistry and materials science, including excited-state processes, charge transfer at catalytic interfaces, and plasmon-mediated photocatalysis, require an accurate treatment of interacting electrons beyond mean-field theory. However, direct solutions of the many-body Schrodinger equation remain computationally intractable for realistic systems due to the exponential growth of the configurational Hilbert space with system size. This challenge motivates the development of reduced representations and embedding strategies capable of retaining essential correlation effects at lower computational cost. The work presented here focuses on stochastic matrix compression and downfolding techniques for many-body electronic structure theory. In particular, new stochastic compression approaches are introduced for the efficient representation of many-body Hamiltonians and correlated wavefunctions within reduced active subspaces. These methods extend stochastic electronic structure techniques beyond their traditional applications in many-body perturbation theory and provide a framework for treating correlated subsystems embedded within large chemical environments. Applications of these approaches are demonstrated across several classes of problems. First, stochastic downfolding methodologies are developed for the computation of charged excitations and Dyson orbitals relevant to catalytic interfaces and molecular spectroscopy. These techniques enable the treatment of large orbital spaces while maintaining accurate descriptions of electron correlation in the active region. Second, stochastic compression methods are applied to the computation of total energies in large solvated and reactive systems, where conventional correlated approaches become prohibitively expensive. Finally, the thesis explores nonequilibrium electronic dynamics at driven catalytic interfaces, including plasmon-assisted charge transfer processes. In this context, time-dependent many-body simulations reveal that transient driving fields can dynamically modify molecular spectral structure, opening additional resonant pathways for hot-carrier injection that are absent in equilibrium descriptions. Taken together, the methods developed in this thesis provide new strategies for reducing the computational complexity of correlated electronic structure calculations while preserving the essential physics of many-body interactions. These results broaden the applicability of stochastic and embedding-based approaches to large-scale equilibrium and nonequilibrium problems in chemistry, condensed matter physics, and materials science.