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Although first principles calculation gives overall electronic structure of each material, it is too much demanding to calculate effects of electron correlation such as fluctuations. Hence, a two-step procedure is often adopted: (1) construction of low-energy model from first principles, and (2) numerical approach for electron correlations in such models. For construction of Hubbard type models, the maximally localized Waniner function (MLWF [1]) are broadly adopted. Recently, not only hopping integrals but also electron interaction parameters, in constrained random phase approximation (cRPA [2]), can be evaluated in first principle. However, MLWF contains some difficulties. In this talk, a model obtained with MLWF and cRPA for a novel nickelate superconductor [3] will be presented. Then, a study in fluctuation exchange approximation [4] comparing the nickelate and a mercury based cuprate will be explained [5]. Subsequently, a new method of model construction based on PMT basis function [6,7], a fusion of the LAPW and LMTO methods, and its application on some simple materials will be introduced.

[1] N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12947 (1997).
[2] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Phys. Rev. B 70, 195104 (2004).
[3] D. Li et al., Nature 572, 624 (2019).
[4] N. E. Bickers, D. J. Scalapino, and S. R. White, Phys. Rev. Lett. 62, 961 (1989).
[5] H. Sakakibara, H. Usui, K. Suzuki, T. Kotani, H. Aoki, and K. Kuroki, Phys. Rev. Lett. 125, 077003 (2020).
[6] T. Kotani and M. van Schilfgaarde, Phys. Rev. B 81, 125117 (2010).
[7] T. Kotani, H. Kino, and H. Akai, J. Phys. Soc. Jpn 84, 034702 (2015).

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