Reproduce “Chebyshev Accelerated Subspace Eigensolver for Pseudo-hermitian Hamiltonians” on OpenResearch

About this paper

Edoardo Di Napoli, Clément Richefort, Xinzhe Wu

An extended Chebyshev Accelerated Subspace iteration Eigensolver (ChASE) computes several thousands of the smallest positive eigenpairs of pseudo-Hermitian Hamiltonians from the Bethe-Salpeter Equation, essential for accurate optoelectronic material simulations. The solver demonstrates quadratic convergence and robust strong scaling on GPU-accelerated systems, achieving up to 4.6 PFLOP/s on 256 GPUs.

Key insights

• The proposed oblique Rayleigh-Ritz variant formally achieves quadratic convergence of Ritz values by ensuring comparable approximation errors for left and right eigenvectors and bounding the inverse overlap parameter.
• The dual basis choice ensures the Rayleigh-Quotient is spectrally equivalent to a Hermitian problem, yielding real Ritz values and preserving the positive-negative spectral symmetry inherent to pseudo-Hermitian Hamiltonians.
• Constraining the initial subspace to the S-positive manifold (e.g., by scaling the lower block of random vectors with a small factor) is critical for numerical stability, preventing failures in the Rayleigh-Ritz procedure.

Summary by alphaXiv.