Shifted COCG method and its application to double orbital extended Hubbard model

TL;DR

The paper introduces the shifted COCG method, an efficient algorithm for solving large linear systems related to many-electron Hamiltonians, demonstrated on a double orbital extended Hubbard model to determine its insulating ground state.

Contribution

It presents the shifted COCG algorithm, which reduces computational cost and memory usage for calculating Green's functions in large-scale quantum many-body problems.

Findings

Successfully applied to a 64 million dimension Hamiltonian

Determined the ground state of the model as an insulator

Reduced memory requirements for large matrix computations

Abstract

We explains the shifted COCG method which can solve a series of the linear equations generated by numbers of scaler shifts, without time consuming matrix-vector operations, except at the only one reference energy. This is a family of the CG method and sharing the robustness and the capability of the accuracy estimation. Then shifted COCG is quite useful to calculate the Green's function of the many-electron Hamiltonian which have very large dimension. We applied it to the double orbital extended Hubbard model with twelve electrons on the periodic sqrt(8) x sqrt(8) site system, the dimension of the Hamiltonian equals to 64,128,064, and found the ground state is insulator. We also explained the crucial points of the shifted COCG algorithm for reducing the amount of required memory.