Targeting specific eigenvectors and eigenvalues of a given Hamiltonian using arbitrary selection criteria

Xia

et al. 2016

Sci Rep

Although the GW approximation is recognized as one of the most accurate theories for predicting materials excited states properties, scaling up conventional GW calculations for large systems remains a major challenge. We present a powerful and simple-to-implement method that can drastically accelerate fully converged GW calculations for large systems, enabling fast and accurate quasiparticle calculations for complex materials systems. We demonstrate the performance of this new method by presenting the results for ZnO and MgO supercells. A speed-up factor of nearly two orders of magnitude is achieved for a system containing 256 atoms (1024 valence electrons) with a negligibly small numerical error of ±0.03 eV. Finally, we discuss the application of our method to the GW calculations for 2D materials.

Section: Resultsmentioning

confidence: 99%

Speeding up GW Calculations to Meet the Challenge of Large Scale Quasiparticle Predictions

Xia

et al. 2016

Sci Rep

The Journal of Chemical Physics

“…[42][43][44] By applying standard iterative methods to the auxiliary operator, it is therefore possible to optimize the interior eigenfunctions of H vib . Out of the different functional forms for Ω ω that have been proposed in the literature, 39,45,46 we will employ the shift-and-invert (S&I) 44,47 and the folded 48 operators. The main advantage of the former is the possibility of exploiting the Harmonic Ritz Values theory 49 to avoid the explicit inversion of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, targeting of pre-selected vibrational levels is achieved by mapping the original Hamiltonian H vib onto an auxiliary operator Ω ω , whose ground state corresponds to one of the interior eigenfunctions of H vib . [42][43][44] By applying standard iterative methods to the auxiliary operator, it is therefore possible to optimize the interior eigenfunctions of H vib . Out of the different functional forms for Ω ω that have been proposed in the literature, 39,45,46 we will employ the shift-and-invert (S&I) 44,47 and the folded 48 operators.…”

Section: Introductionmentioning

confidence: 99%

Optimization of highly excited matrix product states with an application to vibrational spectroscopy

Baiardi

Stein

Barone

et al. 2019

Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their application range. In vibrational spectroscopy, for example, molecules with more than 15 to 20 vibrational modes can hardly be studied. An efficient approximation to the full configuration interaction solution can be obtained with the density matrix renormalization group (DMRG) algorithm without a restriction to a predefined excitation level. In a standard DMRG implementation, however, excited states are calculated with a ground-state optimization in the space orthogonal to all lower lying wave function solutions. A trivial parallelization is therefore not possible and the calculation of highly excited states becomes prohibitively expensive, especially in regions with a high density of states. Here, we introduce two variants of the density matrix renormalization group algorithm that allow us to target directly specific energy regions and therefore highly excited states. The first one, based on shift-and-invert techniques, is particularly efficient for low-lying states, but is not stable in regions with a high density of states. The second one, based on the folded auxiliary operator, is less efficient, but more accurate in targeting highenergy states. We apply the algorithm to the solution of the nuclear Schrödinger equation, but emphasize that it can be applied to the diagonalization of general Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address X-ray spectra. In combination with several root-homing algorithms and a stochastic sampling of the determinant space, excited states of interest can be adequately tracked and analyzed during the optimization. We validate these algorithms by calculating several highly excited vibrational states of ethylene and demonstrate that we can accurately calculate prominent spectral features of large molecules such as the sarcosine-glycine dipeptide. a)

“…As usual, the applied diagonalization methods are not capable of fulfilling this task. Therefore, in this work, we used the Jacobi-Davidson iteration method with a preliminary incomplete LU decomposition of the Hamiltonian [12]. This method makes it possible to calculate only the eigenvalues located within a predetermined interval.…”

Section: Theoretical Modelmentioning

confidence: 99%

Influence of Atomic Disorder on the Auger Recombination Rate in p-InGaN Alloys

Zinovchuk

Sevost’yanov

2020

Ukr. J. Phys.

The influence of the atomic disorder on the Auger recombination rate in p-InGaN alloys has been studied. The disorder was simulated using a 4 × 4 × 4 supercell in which In and Ga atoms taken in a required stoichiometric ratio were randomly distributed over the supercell sites. A comparison between the Auger recombination rates calculated in the framework of the supercell and virtual-crystal approximations showed that a large number of allowed interband transitions induced by the atomic disorder strongly increases the Auger recombination rate in wide-band-gap p-InGaN alloys.