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Ground state properties of the Kondo lattice model with electron-phonon interaction
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| Title: | Ground state properties of the Kondo lattice model with electron-phonon interaction |
| Other Titles: | 電子格子相互作用をもつ近藤格子模型における基底状態の性質 |
| Authors: | 冨永, 隼人 Browse this author |
| Issue Date: | 26-Dec-2022 |
| Publisher: | Hokkaido University |
| Abstract: | It is known that heavy fermion systems exhibit a variety of orderings such
as superconductivity, ferromagnetism, and antiferromagnetism. Therefore, heavy
fermion systems have been actively studied both theoretically and experimentally.
The Kondo lattice model(KLM) is one of the models for heavy fermion systems and
describes the exchange interaction between localized spins and conduction electrons.
Since the KLM has a wide range of applications, there have been various studies
on this model. On the other hand, electron-phonon coupled systems have been
extensively explored because the interaction between electrons and phonons causes
intriguing physical phenomena.
In this thesis, we rigorously analyze the effect of electron-phonon interactions
in heavy fermion systems. More specifically, the magnetic properties of the ground
state of the half-filled KLM with the electron-phonon interaction term are examined
in a rigorous manner. The spin reflection positivity introduced by Lieb is known to
be very effective in analyzing the magnetic properties of the ground states of many
electron systems. However, since the KLM does not have Coulomb interaction
terms, the spin-reflection positivity cannot be directly applied to it. In this thesis,
we show that this difficulty can be overcome by applying Miyao’s operator inequality
theory to the KLM. This enables us to prove that the ground state of the KLM
with the electron-phonon interaction term is unique, and to determine the exact
value of the total spin of the ground state. |
| Conffering University: | 北海道大学 |
| Degree Report Number: | 甲第15223号 |
| Degree Level: | 博士 |
| Degree Discipline: | 理学 |
| Examination Committee Members: | (主査) 教授 宮尾 忠宏, 教授 洞 彰人, 教授 坂井 哲 |
| Degree Affiliation: | 理学院（数学専攻） |
| Type: | theses (doctoral) |
| URI: | http://hdl.handle.net/2115/88173 |
| Appears in Collections: | 課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
学位論文 (Theses) > 博士 （理学）
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