Biorthogonal linear-scaling approach for the transcorrelated method

TL;DR

This paper introduces a biorthogonal linear-scaling algorithm for the transcorrelated method, enabling efficient large-scale first-principles calculations by handling non-Hermitian operators with localized orbitals.

Contribution

It presents a novel biorthogonal linear-scaling approach for the transcorrelated method that manages non-Hermitian Hamiltonians with localized orbitals.

Findings

Achieves linear-scaling behavior in transcorrelated calculations.

Effectively handles non-Hermitian operators with biorthogonal wave functions.

Enables application to larger condensed-matter systems.

Abstract

We develop a biorthogonal linear-scaling algorithm for a transcorrelated method based on the localized nature of transformed orbitals. The transcorrelated method, which employs a similarity-transformed Hamiltonian referred to as a transcorrelated Hamiltonian, enables highly accurate first-principles condensed-matter calculations in principle. Meanwhile, the transcorrelated Hamiltonian numerically prevents us from applying it to large systems because the transcorrelated Hamiltonian is a non-Hermitian operator and contains a 3-body electron-electron interaction term. Non-Hermiticity means that left and right wave functions of the total energy expectation value are different from each other. Namely, a biorthogonal form is required. Our new method allows us to handle the non-Hermitian operator and exhibits a linear-scaling behavior.