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Historically, the `spin Peierls' system was the first macroscopic
system proposed to have a spin gap
[14,15,16]. It consists of an S=1/2
antiferromagnetic spin chain with a spinlattice coupling. If the
lattice is soft in the chain direction, and the chains are magnetically
well separated from each other [17,18], a
periodic deformation (dimerization) of the lattice takes place at a
finite temperature (Fig.3ab).
The lattice dimerization alternatively enhances [] or
reduces [] the antiferromagnetic interactions, and brings
about singlet pair formations on the enhanced exchange links (Fig.3b).
Figure 3:
(a) An S=1/2 spin chain with an uniform antiferromagnetic interaction J.
(b) The lattice dimerized state below the spin Peierls transition temperature .

The ground state structure of the spinPeierls system is a stacking of
singlet pairs along the chain. The ground state is nonmagnetic, because
each singlet pair produces no magnetic field. Since the singlet
pairs are well localized, there is a finite energy gap between the ground
state and the excited states. This system is studied in Chapter 6.
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