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タイトル: Renormalization Group Analysis of Multi-Band Many-Electron Systems at Half-Filling
著者: Kashima, Yohei
キーワード: Many-electron system
renormalization
group
the Hubbard model
zero-temperature limit
発行日: 2016年1月25日
出版者: Graduate School of Mathematical Sciences, The University of Tokyo
掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 23 (2016), No. 1, Page 1–288
抄録: Renormalization group analysis for multi-band manyelectron systems at half-filling at positive temperature is presented. The analysis includes the Matsubara ultra-violet integration and the infrared integration around the zero set of the dispersion relation. The multi-scale integration schemes are implemented in a finitedimensional Grassmann algebra indexed by discrete position-time variables. In order that the multi-scale integrations are justified inductively, various scale-dependent estimates on Grassmann polynomials are established. We apply these theories in practice to prove that for the half-filled Hubbard model with nearest-neighbor hopping on a square lattice the infinite-volume, zero-temperature limit of the free energy density exists as an analytic function of the coupling constant in a neighborhood of the origin if the system contains the magnetic flux π (mod 2π) per plaquette and 0 (mod 2π) through the large circles around the periodic lattice. Combined with Lieb’s result on the flux phase problem ([Lieb, E. H., Phys. Rev. Lett. 73 (1994), 2158]), this theorem implies that the minimum free energy density of the fluxphase problem converges to an analytic function of the coupling constant in the infinite-volume, zero-temperature limit. The proof of the theorem is based on a four-band formulation of the model Hamiltonian and an extension of Giuliani-Mastropietro’s renormalization designed for the half-filled Hubbard model on the honeycomb lattice ([Giuliani, A. and V. Mastropietro, Commun. Math. Phys. 293 (2010), 301–346]).
URI: http://hdl.handle.net/2261/61486
ISSN: 13405705
出現カテゴリ:Journal of Mathematical Sciences, the University of Tokyo
Journal of Mathematical Sciences, the University of Tokyo

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