リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「Geminal theory for strongly correlated few-body systems」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。
リケラボ

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

Geminal theory for strongly correlated few-body systems

川﨑, 愛理 東京大学 DOI:10.15083/0002001849

2021.10.04

概要

To calculate strongly correlated systems accurately, one needs to treat strong and weak correlations simultaneously. Popular methods, such as Hartree-Fock theory or density functional theory, can treat the weak correlation but cannot treat the strong correlation. On the other hand, the full- configuration-interaction (full-CI) method can treat the strong correlation well but it needs high calculation cost. In this context, I focus on the wave function theory for the electron pair. In condensed matter physics, the electron pair is an important concept for superconductivity. Also in the field of chemistry, the concept of electron pair has been used to represent a chemical bond since a long time ago. The electron pair is called geminal in chemistry and many calculation methods using geminal were developed. The method of expressing different chemical bonds using different gem- inals is called antisymmetrized-product-of-geminals (APG) theory. Although the idea of APG was proposed long ago, there are few APG studies because of its high calculation cost and complexity in the calculation.

In this thesis, I overcome the computational difficulty of APG using a tensor decomposition method developed in mathematics and make the variational determination of APG tractable numerically. This makes it possible to analyze the APG wave function with- out introducing additional approximations to the geminals and thus to understand the inherent advantage and disadvantage in describing strongly correlated few-body systems. This understanding helps me to develop a method to incorporate the electron correlation beyond the original APG. This novel method is based on a polynomial extension of APG; note that the original APG has a monomial form. With the polynomial extension, I succeed in relating geminals to the valence bond even in the strong correlation regime. I recognize the polynomial extension as an introduction of the “resonance” effect into the APG-based valence bond theory and thus is a natural improvement.

I also develop variations of the APG calculation. I develop a simplified geminal method, which is different from the ones developed previously in the literatures. I also develop a geminal method specialized for a strongly correlated impurity system embedded in a weakly correlated medium.

The present study analyzes geminal theories comparatively from (a) the simplest one, called antisymmetrized geminal powers (AGP), which is a mean-field theory of geminals, (b) APG and (c) its extension, bridging thereby the HF to full-CI via electron-pair theories of different levels. I believe that the present work has made clearer the property of geminal theory and would stimulate further sophistication of the geminal-based valence bond theory.

論文の公開元へ

関連論文

関連論文をもっと見る

参考文献

[1] P. Hohenberg and W. Kohn, Phys. Rev. 136, 864 (1964).

[2] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

[3] V. I. Anisimov, F. Aryasetiawan, and A. Lichtenstein, Journal of Physics: Condensed Matter 9, 767 (1997).

[4] P. Eva, A. Lichtenstein, D. Vollhardt, and E. Koch, Theoretische Nanoelektronik (2011).

[5] M. Suzuki, Quantum Monte Carlo methods in condensed matter physics (World scientific, 1993).

[6] L. Hedin, Phys. Rev. 139, 796 (1965).

[7] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012).

[8] G. Knizia and G. K.-L. Chan, J. Chem. Theory Comput. 9, 1428 (2013).

[9] F. Coester and H. Ku¨mmel, Nucl. Phys. 17, 477 (1960).

[10] J. Cˇ´ıˇzek, J. Chem. Phys. 45, 4256 (1966).

[11] S. R. White, Phys. Rev. Lett. 69, 2863 (1992).

[12] O¨ . Legeza, J. R¨oder, and B. Hess, Mol. Phys. 101, 2019 (2003).

[13] G. K.-L. Chan and S. Sharma, Annu. Rev. Phys. Chem. 62, 465 (2011).

[14] R. J. Gillespie and I. Hargittai, The VSEPR model of molecular geometry (Courier Corporation, 2013).

[15] A. J. Coleman, J. Math. Phys. 6, 1425 (1965).

[16] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).

[17] W. Kutzelnigg, J. Chem. Phys. 40, 3640 (1964).

[18] P. A. Limacher, P. W. Ayers, P. A. Johnson, S. De Baerdemacker, D. Van Neck, and P. Bultinck, J. Chem. Theory Comput. 9, 1394 (2013).

[19] A. Hurley, J. E. Lennard-Jones, and J. A. Pople, Proc. R. Soc. Lond. A 220, 446 (1953).

[20] A. M. Tokmachev, Int. J. Quantum Chem. 116, 265 (2016).

[21] M. Tarumi, M. Kobayashi, and H. Nakai, Int. J. Quantum Chem. 113, 239 (2013).

[22] D. M. Silver, J. Chem. Phys. 50, 5108 (1969).

[23] N. Onishi and S. Yoshida, Nucl. Phys. 80, 367 (1966).

[24] W. Uemura, S. Kasamatsu, and O. Sugino, Phys. Rev. A 91, 062504 (2015).

[25] T. G. Kolda and B. W. Bader, SIAM review 51, 455 (2009).

[26] O. Goscinski, Int. J. Quantum Chem. 22, 591 (1982).

[27] B. Weiner and O. Goscinski, Phys. Rev. A 27, 57 (1983).

[28] D. A. Mazziotti, Chem. Phys. Lett. 338, 323 (2001).

[29] D. Mazziotti, J. Chem. Phys. 112, 10125 (2000).

[30] K. Hara, S. Iwasaki, and K. Tanabe, Nucl. Phys. A 332, 69 (1979).

[31] H. Shull, J. Chem. Phys. 30, 1405 (1959).

[32] R. G. Parr, F. O. Ellison, and P. G. Lykos, J. Chem. Phys. 24, 1106 (1956).

[33] T. Arai, J. Chem. Phys. 33, 95 (1960).

[34] R. McWeeny and B. Sutcliffe, Proc. R. Soc. Lond. A 273, 103 (1963).

[35] V. A. Nicely and J. F. Harrison, J. Chem. Phys. 54, 4363 (1971).

[36] P. Carrington and G. Doggett, Mol. Phys. 26, 641 (1973).

[37] P. A. Johnson, P. W. Ayers, P. A. Limacher, S. De Baerdemacker, D. Van Neck, and P. Bultinck, Comput. Theor. Chem. 1003, 101 (2013).

[38] P. Jeszenszki, P. R. Nagy, T. Zoboki, A´. Szabados, and P. R. Surj´an, Int. J. Quantum Chem. 114, 1048 (2014).

[39] M. Casula and S. Sorella, J. Chem. Phys. 119, 6500 (2003).

[40] D. Tahara and M. Imada, J. Phys. Soc. Jpn. 77, 114701 (2008).

[41] T. Yanagisawa, M. Miyazaki, and K. Yamaji, Int. J. Mod. Phys. B , 1840023 (2018).

[42] T. Mizusaki and M. Oi, Phys. Lett. B 715, 219 (2012).

[43] B. Zumino, J. Math. Phys. 3, 1055 (1962).

[44] C. Bloch, Nucl. Phys. 39, 95 (1962).

[45] J. Dobaczewski, Phys. Rev. C 62, 017301 (2000).

[46] T. Tsuchimochi, M. Welborn, and T. Van Voorhis, J. Chem. Phys. 143, 024107 (2015).

[47] J. Hubbard, Proc. R. Soc. Lond. A 276, 238 (1963).

[48] R. Pariser and R. G. Parr, J. Chem. Phys. 21, 767 (1953).

[49] J. A. Pople, Trans. Faraday Soc. 49, 1375 (1953).

[50] L. R. Tucker, Psychometrika 31, 279 (1966).

[51] A. Kawasaki and O. Sugino, J. Chem. Phys. 145, 244110 (2016).

[52] A. Kawasaki and O. Sugino, arXiv preprint arXiv:1805.06138 (2018).

[53] L. Oeding and G. Ottaviani, J. Symb. Comput. 54, 9 (2013).

[54] P. Comon and B. Mourrain, Signal Processing 53, 93 (1996).

[55] J. Alexander and A. Hirschowitz, J. Algebr. Geom. 4, 201 (1995).

[56] I. Fischer, Mathematics Magazine 67, 59 (1994).

[57] H. Lee, Linear Algebra Its Appl. 492, 89 (2016).

[58] D. G. Glynn, Eur. J. Combin. 31, 1887 (2010).

[59] H. Derksen, Foundations of Computational Mathematics 16, 779 (2016).

[60] W. Squire and G. Trapp, SIAM review 40, 110 (1998).

[61] E. Neuscamman, J. Chem. Phys. 139, 194105 (2013).

[62] E. Neuscamman, Communication: A jastrow factor coupled cluster theory for weak and strong electron correlation, 2013.

[63] Y. Luo, A. Zen, and S. Sorella, J. Chem. Phys. 141, 194112 (2014).

[64] A. Zen, Y. Luo, G. Mazzola, L. Guidoni, and S. Sorella, J. Chem. Phys. 142, 144111 (2015).

[65] Y. N. Dauphin, R. Pascanu, C. Gulcehre, K. Cho, S. Ganguli, and Y. Bengio, Iden- tifying and attacking the saddle point problem in high-dimensional non-convex op- timization, in Advances in neural information processing systems, pp. 2933–2941, 2014.

[66] M. Kawamura, K. Yoshimi, T. Misawa, Y. Yamaji, S. Todo, and N. Kawashima, Computer Physics Communications 217, 180 (2017).

[67] T. Misawa, S. Morita, K. Yoshimi, M. Kawamura, Y. Motoyama, I. Kota, T. Ohgoe, M. Imada, and T. Kato, Comput. Phys. Commun. (2018).

[68] E. Pastorczak and K. Pernal, Physical Chemistry Chemical Physics 17, 8622 (2015).

[69] J. Nguyen, Bachelor Thesis (2008).

[70] K. Penc and F. Mila, Physical Review B 50, 11429 (1994).

[71] T. Verstraelen, P. Tecmer, F. Heidar-Zadeh, C. E. Gonz´alez-Espinoza, M. Chan, T. D. Kim, K. Boguslawski, S. Fias, S. Vandenbrande, D. Berrocal, and P. W. Ayers, Horton 2.1.0, http://theochem.github.com/horton/, 2017.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文
を
一発検索！

この論文の関連論文を見る