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2020년 11월 13일 (금) 01:35 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
encyclopedia
books
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.