Path-Integral Renormalization Group Treatments for Many-Electron Systems with Long-Range Repulsive Interactions

TL;DR

This paper introduces an efficient path-integral renormalization group algorithm for many-electron systems with long-range Coulomb interactions, reducing computational costs and enabling practical simulations.

Contribution

It develops a Green's function-free algorithm within the PIRG framework for realistic electron systems with long-range interactions.

Findings

Significant reduction in CPU time for calculations

Successful application to systems with long-range Coulomb interactions

Potential for practical numerical simulations of complex electron systems

Abstract

A practical algorithm for many-electron systems based on the path-integral renormalization group (PIRG) method is proposed in the real-space finite-difference (RSFD) approach. The PIRG method, developed for investigating strongly correlated electron systems, has been successfully applied to some models such as Hubbard models. However, to apply this method to more realistic systems of electrons with long-range Coulomb interactions within the RSFD formalism, the one-body Green's function, which requires large computational resources, is to be replaced with an alternative. For the same reason, an efficient algorithm for computing the Fock matrix is needed. The newly proposed algorithm is free of the one-body Green's function and enables us to compute the Fock matrix efficiently. Our result shows a significant reduction in CPU time and the possibility of using the present algorithm as a practical numerical tool.