Theory of spin‐Peierls transition in Heisenberg and Hubbard models

A spin‐lattice dimerization occurring in a system of one‐dimensional (1D) magnetic spins coupled to the lattice (Spin‐Peierls instability) is studied for classical and quantum Heisenberg and for one‐ and two‐band Hubbard models. Using the exact solutions it is shown for the classical case that second or first order lattice phase transitions (PT) are possible. For the isotropic quantum s=1/2 Heisenberg and Hubbard models using the variational principle it is shown that PT can only be of second order while the spin anisotropy and the presence of a second electronic band yield the first order PT. Some applications to PT in VO2 are also made.