Symbol

Meaning

Def. Equation

$\widehat{H}$

Hamiltonian of our model

(1)

$\widehat{T}$

Kinetic term of $\widehat{H}$

(2)

${\widehat{V}}_B$

Potential term of $\widehat{H}$

(3)

B

Strength of ${\widehat{V}}_B$

(3)

${\widehat{V}}_{k{k}^{\prime }}$

Local interaction of ${\widehat{V}}_B$

(4)

${\theta }_k\mathrm{,}{\varphi }_k$

Angle variables at site k

$|l_k\mathrm{,}{m}_k\rangle$

State of quantum numbers $l\mathrm{,}m$ at site k

(5)

${\widehat{L}}_{\alpha \mathrm{,}k}$

Angular momentum operators

$N_s$

Total number of sites

$\theta$

Average angle of ${\theta }_k$

(11)

$\varphi$

Average angle of ${\varphi }_k$

(11)

$a_{jk}$

Matrix element of orthogonal trans.

(13)

${\xi }_j$

Angle by orthogonal trans. of ${\theta }_k$

(14)

${\chi }_j$

Angle by orthogonal trans. of ${\varphi }_k$

(14)

${\widehat{L}}_{\xi \mathrm{,}\alpha \mathrm{,}k}$

Operators by orthogonal trans. of ${\widehat{L}}_{\alpha \mathrm{,}k}$

(19)

${\tilde{\xi }}_j$

Variable changed from ${\xi }_j$

(22)

${\eta }_j$

Variable changed from ${\chi }_j$

(22)

${\widehat{L}}_{A\mathrm{,}\pm }$

Effective op. of angular mo. with ± compo.

(21)

${\widehat{L}}_{\varphi }$

Effective op. of angular mo. with z compo.

(26)

${\widehat{H}}_A$

Effective Hamiltonian for large B

(28)

$|{\Psi }_0\rangle$

Ground state for $B=0$

(30)

J

Quantum number of total angular momentum

$E_J$

Lowest energy of J

$n_{link}$

Link number of one site

$l_{\max }$

Maximum of $l$ in numerical calculations

Section 4.1

${\widehat{H}}_{A\mathrm{,2}}$

Effective Hamiltonian of two particles

(46)