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The zero-temperature limit of the free energy density in many-electron systems at half-filling
http://hdl.handle.net/2261/00074373
http://hdl.handle.net/2261/000743738075894b-c7ad-41b5-b99a-ed25f233cd9e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms240101.pdf (962.0 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2018-04-04 | |||||
| タイトル | ||||||
| タイトル | The zero-temperature limit of the free energy density in many-electron systems at half-filling | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | many-electron system | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | renormalization group | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | zero-temperature limit | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Kashima, Yohei
× Kashima, Yohei |
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| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We prove by means of a renormalization group method that in weakly interacting many-electron systems at half-filling on a periodic hyper-cubic lattice, the free energy density uniformly converges to an analytic function of the coupling constants in the infinite-volume, zero-temperature limit if the external magnetic field has a chessboard-like flux configuration. The spatial dimension is allowed to be any number larger than 1. The system covers the Hubbard model with a nearest-neighbor hopping term, on-site interactions, exponentially decaying density-density interactions and exponentially decaying spin-spin interactions. The magnetic field must be included in the kinetic term by the Peierls substitution. The flux configuration and the sign of the nearest-neighbor density-density/spin-spin interactions can be adjusted so that the free energy density is minimum among all the flux configurations. Consequently, the minimum free energy density is proved to converge to an analytic function of the coupling constants in the infinite-volume, zero-temperature limit. These are extension of the results on a square lattice in the preceding work ([Kashima, Y., ``The special issue for the 20th anniversary'', J. Math. Sci. Univ. Tokyo. 23 (2016), 1-288]). We refer to lemmas proved in the reference in order to complete the proof of the main results of this paper. So this work is a continuation of the preceding work. | |||||
| 書誌情報 |
Journal of Mathematical Sciences, The University of Tokyo 巻 24, 号 1, p. 1-158, 発行日 2017-02-17 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| 著者版フラグ | ||||||
| 値 | publisher | |||||
| Mathmatical Subject Classification | ||||||
| 81T17(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 81T28(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2015-09-01 | ||||||
