Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies

Vlček, Vojtěch

doi:10.1021/acs.jctc.9b00317

Cited by 35 publications

(45 citation statements)

References 86 publications

(272 reference statements)

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“…For nanoscale systems with thousands of atoms, ∼ 100 samples suffice to represent the GF, with only ∼ 10 needed to represent δn(r, t). [57,58,60] The stochastic methodology capitalizes on the fact that the key quantities (G and W ) are determined by collective properties, which are inherently low-rank and captured by the dynamics of a few (random) states within the Hilbert space. This approach leads to a linear scaling algorithm that can treat thousands of atoms.…”

Section: A Stochastic Many-body Theorymentioning

confidence: 99%

“…In this work, we overcome these limitations: we pro-pose two new developments in the stochastic many-body perturbation theory (MBPT) techniques [57][58][59][60][61][62] which can readily elucidate how the electronic structure behaves in giant moiré systems. We investigate tBLG with a large twist angle of θ ≈ 6 • (with 2184 atoms, i.e., 8736 valence electrons), which is weakly correlated at ambient conditions but develops flat bands at high compressions.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic many-body calculations of moiré states in twisted bilayer graphene at high pressures

Romanova¹,

Vlček²

2021

Preprint

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Twisted bilayer graphene (tBLG) hosts correlated electrons in flat bands, stemming from the coupling between mutually rotated monolayers. In this work, we develop new stochastic manybody techniques addressing the weakly and strongly correlated electrons and explore the pressureinduced correlations in moiré states. For the first time, it is thus possible to address the behavior of twisted bilayer with giant unit cells via ab-initio many-body theory. The calculations document the formation of charge carrier localization at the Fermi level while most weakly correlated states are merely shifted in energy. This contrasts with mean-field results. The correlated subspace is mapped on a Hubbard model with a screened frequency dependent on-site interaction, which ranges between 65 and 300 meV under compression. The Dyson orbitals exhibit spatial distribution similar to the mean-field single particle states but yield smaller on-site terms. Under pressure, the on-site interaction increases, dominated by bare Coulomb interaction, while screening does not change. The correlated moiré states thus appear effectively unscreened at high pressures suggesting the presence of insulating states in compressed tBLG.

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Section: A Stochastic Many-body Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic many-body calculations of moiré states in twisted bilayer graphene at high pressures

Romanova¹,

Vlček²

2021

Preprint

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“…43,75,76 Nevertheless, the GW correlation neglects the quantum fluctuations, which may become important for high energy excitations and/or for unoccupied states. 64,77 The method of subspace separations is, however, general and applicable to beyond-GW approaches; it will be explored in the future. Here, a single-shot perturbative correction is computed within the random phase approximation (RPA) on top of a density functional theory (DFT) starting point (see the SI for details).…”

Section: Stochastic Calculation Of the Self-energymentioning

confidence: 99%

“…[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] Further, the methodology is open for systematic improvements; embedding within the GF framework 21,43,47,48,54,60 is conceptually straightforward and "seamless." Finally, recent developments of stochastic GF methods [60][61][62][63][64] enabled calculations for giant systems with thousands of electrons, practically treating large and inhomogeneous systems on equal footing.…”

Section: Introductionmentioning

confidence: 99%

Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory

Weng,

Vlcek

2021

Preprint

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Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells representing the solvated systems are inexpensive and require ∼ 1000 CPU•hrs. We find that the coupling with the environment accounts for ∼ 40% of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the QP energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments.

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“…"Vertex correc- tions" to GW has a long history. Several different types of vertex corrections have been proposed and tested [26,36,37,41,[44][45][46][47][48][49][50][51][52][53][54][55]. Despite considerable efforts, none of these vertexcorrections have yet found wide-spread use in production calculations.…”

Section: Introductionmentioning

confidence: 99%

Assessing the $G_0W_0Γ^{(1)}_0$ approach: Beyond $G_0W_0$ with Hedin's full second-order self-energy contribution

Wang,

Rinke,

Ren

2021

Preprint

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We present a self-energy approach for quasiparticle energy calculations that goes beyond Hedin's GW approximation by adding the full second-order self-energy (FSOS-W ) contribution. The FSOS-W diagram involves two screened Coulomb interaction (W ) lines and adding the FSOS-W to the GW self-energy can be interpreted as first-order vertex correction to GW (GW Γ (1) ). Our FSOS-W implementation is based on the resolution-ofidentity technique and exhibits better than O(N 5 ) scaling with system size for small to medium-sized molecules. We then present one-shot GW Γ (1) (G 0 W 0 Γ(1) 0 ) benchmarks for the GW 100 test set and a set of 24 acceptor molecules. For semilocal or hybrid density functional theory starting points, G 0 W 0 Γ(1) 0 systematically outperforms G 0 W 0 for the first vertical ionization potentials (vIPs) and electron affinities (vEAs) of both test sets. Finally, we demonstrate that a static FSOS-W self-energy significantly underestimates the quasiparticle energies.

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Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies

Cited by 35 publications

References 86 publications

Stochastic many-body calculations of moiré states in twisted bilayer graphene at high pressures

Stochastic many-body calculations of moiré states in twisted bilayer graphene at high pressures

Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory

Assessing the $G_0W_0Γ^{(1)}_0$ approach: Beyond $G_0W_0$ with Hedin's full second-order self-energy contribution

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