Hubbard model

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
  \(\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}\), \(j=1,\cdots, N\)
  \(\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u}\), \(l=1,\cdots, M\)
  

 

 

 

 

 

 

history

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

 

 

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encyclopedia

• http://en.wikipedia.org/wiki/Hubbard_model
• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

• The One-Dimensional Hubbard Model
• 2010년 books and articles
  
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

articles

• Lax Pair for the One-Dimensional Hubbard Model
  
  • Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu, 1986
    
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://pythagoras0.springnote.com/
• 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
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표 현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/