Peierls instability in Heisenberg chains

Dimerization phase transitions for $S=\frac{1}{2}$ linear antiferromagnetic chains is investigated by analogy with Peirels transitions in linear conducting chains. This analogy is very close when the fermion representation is used to describe the spin system, and the fermion interactions are treated in the Hartree-Fock approximation. Since the Fermi wave vector can be varied continuously by a magnetic field, the linear antiferromagnetic chain may be a convenient system for studying questions concerning. the commensurability of the Fermi wave vector with the underlying lattice which have arisen in connection with the conventional Peierls transition.