"Hubbard model"의 두 판 사이의 차이

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2번째 줄: 2번째 줄:
  
 
* 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 Wu
 
** application of Bethe ansatz
 
** application of Bethe ansatz
 
*  1972 Takahasi
 
*  1972 Takahasi

2013년 6월 28일 (금) 05:08 판

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



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