Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance

Abstract

We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-Hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

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References in corpus (21)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Yambo: an \textit{ab initio} tool for excited state calculations
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Ab initio calculation of excitonic effects in the optical spectra of semiconductors
• GPAW: An open Python package for electronic-structure calculations
• Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators
• Questaal: a package of electronic structure methods based on the linear muffin-tin orbital technique
• Exciton-plasmon states in nanoscale materials: breakdown of the Tamm-Dancoff approximation
• Theory of phonon-assisted luminescence in solids: application to hexagonal boron nitride
• Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation
• Exciton lifetime and optical linewidth profile via exciton-phonon interactions: Theory and first-principles calculations for monolayer MoS${}_2$
• Structure Preserving Parallel Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem
• SIMPLE code: optical properties with optimal basis functions
• Non-adiabatic exciton-phonon coupling in Raman spectroscopy of layered materials
• A structure preserving Lanczos algorithm for computing the optical absorption spectrum
• Fast optical absorption spectra calculations for periodic solid state systems
• Excitonic response in TMD heterostructures from first-principles: impact of stacking, twisting, and interlayer distance
• Theory of resonant Raman scattering: Toward a comprehensive \textit{ab initio} description
• Efficient On-the-Fly Interpolation Technique for Bethe-Salpeter Calculations of Optical Spectra
• High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem
• Excitons under strain: light absorption and emission in strained hexagonal boron nitride