| ATOMIC AND MOLECULAR PHYSICS |
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Random Green's Function Method for Large-Scale Electronic Structure Calculation |
| Mingfa Tang1, Chang Liu2, Aixia Zhang1, Qingyun Zhang1, Jiayu Zhai3, Shengjun Yuan4,5, and Youqi Ke1* |
1School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
2Xiaogan Sichuang Information Technology Co., LTD, Xiaogan 432000, China
3Institute of Mathematical Sciences, ShanghaiTech University, Shanghai 201210, China
4Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, and School of Physics and Technology, Wuhan University, Wuhan 430072, China
5Wuhan Institute of Quantum Technology, Wuhan 430206, China
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| Cite this article: |
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Mingfa Tang, Chang Liu, Aixia Zhang et al 2024 Chin. Phys. Lett. 41 053102 |
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Abstract We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H$_{2}$O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H$_{2}$O clusters at $T=0$ K can reach an error of $\sim$ $1$ meV per H$_{2}$O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.
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Received: 17 April 2024
Express Letter
Published: 28 April 2024
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