"Hubbard model"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “* Princeton companion to mathematics(Companion_to_Mathematics.pdf)” 문자열을 “” 문자열로) |
imported>Pythagoras0 |
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* The Hubbard model describes hopping electrons on a lattice | * The Hubbard model describes hopping electrons on a lattice | ||
| − | * 1968 Lieb and We | + | * 1968 Lieb and We |
** application of Bethe ansatz | ** application of Bethe ansatz | ||
| − | * 1972 Takahasi | + | * 1972 Takahasi |
** string hypothesis | ** string hypothesis | ||
** replace the Lieb-Wu equations by simpler ones | ** replace the Lieb-Wu equations by simpler ones | ||
| 10번째 줄: | 10번째 줄: | ||
* algebraic Bethe ansatz for the Hubbard model | * algebraic Bethe ansatz for the Hubbard model | ||
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==Lieb-Wu equations== | ==Lieb-Wu equations== | ||
| + | * describing Eigenstates of the Hubbard Hamiltonian | ||
| + | * [[Bethe ansatz]] equation | ||
| + | :<math>\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u},\,j=1,\cdots, N</math> | ||
| + | :<math>\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u},\,l=1,\cdots, M</math> | ||
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==string hypothesis== | ==string hypothesis== | ||
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==history== | ==history== | ||
| 36번째 줄: | 38번째 줄: | ||
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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==related items== | ==related items== | ||
| + | * [[Bethe ansatz]] | ||
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==encyclopedia== | ==encyclopedia== | ||
* http://en.wikipedia.org/wiki/Hubbard_model | * http://en.wikipedia.org/wiki/Hubbard_model | ||
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==books== | ==books== | ||
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* [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521802628 The One-Dimensional Hubbard Model] | * [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521802628 The One-Dimensional Hubbard Model] | ||
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==articles== | ==articles== | ||
| − | * [http://dx.doi.org/10.1143/JPSJ.56.1340 Lax Pair for the One-Dimensional Hubbard Model] | + | * Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu[http://dx.doi.org/10.1143/JPSJ.56.1340 Lax Pair for the One-Dimensional Hubbard Model], 1986 |
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[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 6월 28일 (금) 05:08 판
introduction
- The Hubbard model describes hopping electrons on a lattice
- 1968 Lieb and We
- application of Bethe ansatz
- 1972 Takahasi
- string hypothesis
- replace the Lieb-Wu equations by simpler ones
- proceeded to drive a set of non-linear integral equations known as thermodynamic Bethe ansatz equations
- algebraic Bethe ansatz for the Hubbard model
Lieb-Wu equations
- describing Eigenstates of the Hubbard Hamiltonian
- Bethe ansatz equation
\[\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u},\,j=1,\cdots, N\] \[\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u},\,l=1,\cdots, M\]
string hypothesis
history
encyclopedia
books
articles
- Miki Wadati, Eugenio Olmedilla and Yasuhiro AkutsuLax Pair for the One-Dimensional Hubbard Model, 1986