Biorthogonal linear-scaling approach for the transcorrelated method

Details Biorthogonal linear-scaling approach for the transcorrelated method Biorthogonal linear-scaling approach for the transcorrelated method

2009-06-16

arxiv.org/abs/0906.2982v1

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

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.

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