- (1)
- decompose the
*S*=1 spins at each site into two*S*=1/2 spins (Fig.35a) - (2)
- make singlet bonds between adjacent
*S*=1/2 spins (Fig.35b) - (3)
- symmetrize the two
*S*=1/2's on each site to restore the*S*=1 degrees of freedom (Fig.35c).

The VBS ground state is non-magnetic singlet in nature, as it is built from many singlet pairs. From numerical calculations of the VBS Hamiltonian (eq.41) with arbitrary magnitudes of the biquadratic term (1/3), it has been shown that the non-magnetic ground state of the pure Heisenberg model () belongs to the same category as the VBS ground state [63,64].

Another characteristic of the VBS state appears when a spin site is
substituted with a foreign ion (Fig.35d). The
foreign ion breaks two singlet pairs, and introduces two *S*=1/2
paramagnetic spins. The *S*=1/2 degrees of freedom have actually been
observed in electron spin resonance (ESR) measurements of a Haldane
material NENP (see section 5.1.4).