Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem

Shao, Meiyue; Jornada, Felipe H. da; Yang, Chao; Deslippe, Jack; Louie, Steven G.

doi:10.1016/j.laa.2015.09.036

Cited by 49 publications

(73 citation statements)

References 33 publications

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“…We find that the TDA consistently underestimates the exciton binding energies compared to the full calculation. This is consistent with the known fact that the TDA overestimates BSE eigenvalues [14]. Secondly, the magnitude of the E b underestimation by the TDA is small for semiconductors, but large for insulators.…”

Section: Tda and Exciton Binding Energiessupporting

confidence: 88%

“…Usually, this is done within the Tamm-Dancoff approximation (TDA), which neglects the coupling between resonant and anti-resonant excitations. There are some recent studies investigating the performance of the TDA for the BSE [13,14]; however, the extent to which the TDA affects the solution of the excitonic Casida equation has not been studied in detail.…”

Section: Introductionmentioning

confidence: 99%

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Excitons in Solids from Time-Dependent Density-Functional Theory: Assessing the Tamm-Dancoff Approximation

Byun

Ullrich

2017

Computation

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Excitonic effects in solids can be calculated using the Bethe-Salpeter equation (BSE) or the Casida equation of time-dependent density-functional theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which decouples excitations and de-excitations, is widely used to reduce computational cost. Here, we study the effect of the TDA on exciton binding energies of solids obtained from the Casida equation using long-range-corrected (LRC) exchange-correlation kernels. We find that the TDA underestimates TDDFT-LRC exciton binding energies of semiconductors slightly, but those of insulators significantly (i.e., by more than 100%), and thus it is essential to solve the full Casida equation to describe strongly bound excitons. These findings are relevant in the ongoing search for accurate and efficient TDDFT approaches for excitons.

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Section: Tda and Exciton Binding Energiessupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Excitons in Solids from Time-Dependent Density-Functional Theory: Assessing the Tamm-Dancoff Approximation

Byun

Ullrich

2017

Computation

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“…In the TDA, the B term that couples excitations to deexcitations is neglected to gain computational efficiency, and hence the BSE decouples into two equations. Here, we perform calculations both with and without the TDA (41).…”

Section: Methodsmentioning

confidence: 99%

“…We solve the BSE Hamiltonian using a generalized non-Hermitian matrix solver, as discussed in ref. 41.…”

Section: Methodsmentioning

confidence: 99%

Low-lying excited states in crystalline perylene

Rangel

Rinn

Sharifzadeh

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Organic materials are promising candidates for advanced optoelectronics and are used in light-emitting diodes and photovoltaics. However, the underlying mechanisms allowing the formation of excited states responsible for device functionality, such as exciton generation and charge separation, are insufficiently understood. This is partly due to the wide range of existing crystalline polymorphs depending on sample preparation conditions. Here, we determine the linear optical response of thin-film single-crystal perylene samples of distinct polymorphs in transmission and reflection geometries. The sample quality allows for unprecedented high-resolution spectroscopy, which offers an ideal opportunity for judicious comparison between theory and experiment. Excellent agreement with firstprinciples calculations for the absorption based on the GW plus Bethe-Salpeter equation (GW-BSE) approach of many-body perturbation theory (MBPT) is obtained, from which a clear picture of the low-lying excitations in perylene emerges, including evidence of an exciton-polariton stopband, as well as an assessment of the commonly used Tamm-Dancoff approximation to the GW-BSE approach. Our findings on this well-controlled system can guide understanding and development of advanced molecular solids and functionalization for applications. molecular crystals | many-body perturbation theory | excited states | spectroscopy

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“…Detailed discussion on these properties can be found in [5,27,29]. Although a definite BSH matrix H defined in (1) is in general non-Hermitian, it is diagonalizable and has real spectrum.…”

Section: Properties Of Definite Bethe-salpeter Hamiltonian Matricesmentioning

confidence: 99%

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

Shao

Jornada

Lin

et al. 2016

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We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of BetheSalpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

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Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem

Cited by 49 publications

References 33 publications

Excitons in Solids from Time-Dependent Density-Functional Theory: Assessing the Tamm-Dancoff Approximation

Excitons in Solids from Time-Dependent Density-Functional Theory: Assessing the Tamm-Dancoff Approximation

Low-lying excited states in crystalline perylene

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

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