"Heisenberg spin1/2 XXX chain"의 두 판 사이의 차이

2011년 1월 6일 (목) 08:23 판

Hamiltonian of XXX spin chain with anisotropic parameter \(\Delta=1\)
\(\hat H = \sum_{j=1}^{N} (\sigma_j^x \sigma_{j+1}^x +\sigma_j^y \sigma_{j+1}^y + \sigma_j^z \sigma_{j+1}^z)\)
two body scattering term
\(s_{jl}=1-2\Delta e^{ik_l}+ e^{ik_l+ik_j}=1-2e^{ik_l}+ e^{ik_l+ik_j}\)
equation satisfied by wave numbers
\(\exp(ik_jN)=(-1)^{N-1}\prod_{l=1}^{N}\exp(-i\theta(k_j,k_l))\)
where
\(\theta(p,q)\) is defined as
\(\exp(-i\theta(p,q))=\frac{1-2\Delta e^{ip}+e^{i(p+q)}}{1-2\Delta e^{iq}+e^{i(p+q)}}=\frac{1-e^{ip}+e^{i(p+q)}}{1- e^{iq}+e^{i(p+q)}}\)
fundamental equation
\(k_jN=2\pi I(k_j)+\sum_{l=1}^{N}\theta(k_j,k_l)\)

@@ 1번째 줄: / 1번째 줄: @@
 <h5>introduction</h5>
+*  Hamiltonian of XXX spin chain with  anisotropic parameter <math>\Delta=1</math><br><math>\hat H = \sum_{j=1}^{N} (\sigma_j^x \sigma_{j+1}^x +\sigma_j^y \sigma_{j+1}^y +  \sigma_j^z \sigma_{j+1}^z)</math><br>
+*  two body scattering term<br><math>s_{jl}=1-2\Delta e^{ik_l}+ e^{ik_l+ik_j}=1-2e^{ik_l}+ e^{ik_l+ik_j}</math><br>
+*  equation satisfied by wave numbers<br><math>\exp(ik_jN)=(-1)^{N-1}\prod_{l=1}^{N}\exp(-i\theta(k_j,k_l))</math><br> where<br><math>\theta(p,q)</math> is defined as<br><math>\exp(-i\theta(p,q))=\frac{1-2\Delta e^{ip}+e^{i(p+q)}}{1-2\Delta e^{iq}+e^{i(p+q)}}=\frac{1-e^{ip}+e^{i(p+q)}}{1- e^{iq}+e^{i(p+q)}}</math><br>
+*  fundamental equation<br><math>k_jN=2\pi I(k_j)+\sum_{l=1}^{N}\theta(k_j,k_l)</math><br>