"Hubbard model"의 두 판 사이의 차이

2021년 2월 17일 (수) 02:07 기준 최신판

introduction

The Hubbard model describes hopping electrons on a lattice
1968 Lieb and Wu
- 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

http://www.google.com/search?hl=en&tbs=tl:1&q=

related items

encyclopedia

http://en.wikipedia.org/wiki/Hubbard_model

books

The One-Dimensional Hubbard Model

articles

de Leeuw, Marius, and Vidas Regelskis. “An Algebraic Approach to the Hubbard Model.” arXiv:1509.06205 [cond-Mat, Physics:hep-Th, Physics:math-Ph, Physics:nlin], September 21, 2015. http://arxiv.org/abs/1509.06205.
Popkov, Vladislav, and Tomaz Prosen. “Infinitely Dimensional Lax Structure for One-Dimensional Hubbard Model.” arXiv:1501.02230 [cond-Mat, Physics:math-Ph, Physics:nlin], January 9, 2015. http://arxiv.org/abs/1501.02230.
Wadati, Miki, Eugenio Olmedilla, and Yasuhiro Akutsu. “Lax Pair for the One-Dimensional Hubbard Model.” Journal of the Physical Society of Japan 56, no. 4 (April 15, 1987): 1340–47. doi:10.1143/JPSJ.56.1340.

메타데이터

위키데이터

ID : Q1571298

Spacy 패턴 목록

[{'LOWER': 'hubbard'}, {'LEMMA': 'model'}]

@@ 2번째 줄: / 2번째 줄: @@
 * The Hubbard model describes hopping electrons on a lattice
-*  1968 Lieb and We<br>
+*  1968 Lieb and Wu
 ** application of Bethe ansatz
-*  1972 Takahasi<br>
+*  1972 Takahasi
 ** string hypothesis
 ** replace the Lieb-Wu equations by simpler ones
@@ 10번째 줄: / 10번째 줄: @@
 * algebraic Bethe ansatz for the Hubbard model
 ==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>
-*  describing Eigenstates of the Hubbard Hamiltonian<br><math>\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}</math>, <math>j=1,\cdots, N</math><br><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}</math>, <math>l=1,\cdots, M</math><br>
 ==string hypothesis==
 ==history==
@@ 36번째 줄: / 38번째 줄: @@
 * http://www.google.com/search?hl=en&tbs=tl:1&q=
 ==related items==
+* [[Bethe ansatz]]
+* [[Bose-Hubbard Model]]
-*
+==encyclopedia==
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia==
 * http://en.wikipedia.org/wiki/Hubbard_model
-* http://en.wikipedia.org/wiki/
-* http://www.scholarpedia.org/
-* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 ==books==
 * [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521802628 The One-Dimensional Hubbard Model]
-* [[2010년 books and articles]]<br>
-* http://gigapedia.info/1/
-* http://gigapedia.info/1/
-* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles==
-* [http://dx.doi.org/10.1143/JPSJ.56.1340 Lax Pair for the One-Dimensional Hubbard Model]<br>
-**  Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu, 1986<br>
-* http://www.ams.org/mathscinet
-* http://www.zentralblatt-math.org/zmath/en/
-* http://arxiv.org/
-* http://pythagoras0.springnote.com/
-* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
-* http://dx.doi.org/10.1143/JPSJ.56.1340
-==question and answers(Math Overflow)==
-* http://mathoverflow.net/search?q=
-* http://mathoverflow.net/search?q=
-==blogs==
-*  구글 블로그 검색<br>
-** http://blogsearch.google.com/blogsearch?q=
-** http://blogsearch.google.com/blogsearch?q=
-==experts on the field==
-* http://arxiv.org/
+==articles==
+* de Leeuw, Marius, and Vidas Regelskis. “An Algebraic Approach to the Hubbard Model.” arXiv:1509.06205 [cond-Mat, Physics:hep-Th, Physics:math-Ph, Physics:nlin], September 21, 2015. http://arxiv.org/abs/1509.06205.
+* Popkov, Vladislav, and Tomaz Prosen. “Infinitely Dimensional Lax Structure for One-Dimensional Hubbard Model.” arXiv:1501.02230 [cond-Mat, Physics:math-Ph, Physics:nlin], January 9, 2015. http://arxiv.org/abs/1501.02230.
+* Wadati, Miki, Eugenio Olmedilla, and Yasuhiro Akutsu. “Lax Pair for the One-Dimensional Hubbard Model.” Journal of the Physical Society of Japan 56, no. 4 (April 15, 1987): 1340–47. doi:[http://dx.doi.org/10.1143/JPSJ.56.1340 10.1143/JPSJ.56.1340].
-==links==
+[[분류:integrable systems]]
+[[분류:math and physics]]
+[[분류:migrate]]
-* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
+==메타데이터==
-* [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내]
+===위키데이터===
-* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
+* ID :  [https://www.wikidata.org/wiki/Q1571298 Q1571298]
-* http://functions.wolfram.com/
+===Spacy 패턴 목록===
+* [{'LOWER': 'hubbard'}, {'LEMMA': 'model'}]