Diagonalization-Free Chebyshev Expansion Methods to Accelerate Mixed Stochastic-Deterministic GW Calculations

Many-body perturbation theory within the GW approximation to the quasiparticle self-energy is the state-of-the-art method for computing quasiparticle properties in materials such as band structures and lifetimes. Previously, we developed a mixed-stochastic deterministic method to significantly accelerate GW calculations within a sum-over-bands formalism by reducing the computational complexity from quartic to quasi-quadratic [1]. The method is based on the construction of random linear combinations of mean-field eigenstates, coined stochastic pseudobands. Due to the dramatic computational savings, the bottleneck in practical GW calculations at scale (> ~1000 atoms) is now the diagonalization of the mean-field Hamiltonian, a practical prerequisite to this method. Here, we present a novel approach to enable the construction of stochastic pseudobands without the need to explicitly diagonalize the DFT Hamiltonian using spectral slicing [2,3]. We employ the Chebyshev-Jackson expansion to construct filters over various energy subspaces of the Hilbert space. We show that the number of matrix-vector products required for such an expansion is weakly dependent on system size enabling one to much more easily perform large-scale GW calculations. We benchmark this approach on a variety of systems of varying sizes and demonstrate the ability to consistently achieve errors in the quasiparticle energies on the order of 20 meV. We envision this approach will be particularly appealing for GW calculations on large systems such as those involving defects, interfaces, or more complicated calculations of surface chemistry and novel low-dimensional materials.

[1] Altman, A. R., Kundu, S., & da Jornada, F. H. (2024). Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations. Physical Review Letters, 132(8), 086401.

[2] G. Schofield, J. R. Chelikowsky, and Y. Saad, A Spectrum Slicing Method for the Kohn–Sham Problem, Computer Physics Communications 183, 497 (2012).

[3] A. Weiße, G. Wellein, A. Alvermann, and H. Fehske, The Kernel Polynomial Method, Rev. Mod. Phys. 78, 275 (2006).