Convergence of adaptive compression methods for Hartree-Fock-like equations

TL;DR

This paper analyzes the adaptive compression method for Hartree-Fock-like equations, establishing its convergence properties and potential for broad application in quantum physics, chemistry, and materials science.

Contribution

It provides a rigorous convergence analysis of the adaptive compression method, highlighting its effectiveness for solving linear eigenvalue problems in quantum applications.

Findings

Proves convergence of the adaptive compression method.

Shows potential for wide application in quantum physics and chemistry.

Provides theoretical foundation for adaptive operator compression techniques.

Abstract

The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator that is possibly dense and full-rank. In this paper, we present a detailed study of the adaptive compression operation and establish rigorous convergence properties of the adaptive compression method in the context of solving linear eigenvalue problems. Our analysis also elucidates the potential use of the adaptive compression method in a wide range of problems.