Real-space treatment of spin-Peierls transitions: Gap equation and magnetic crossover of the linear Heisenberg antiferromagnet

The spin-Peierls transition at TSP of s = 1/2 Heisenberg antiferromagnetic chains with linear spin–phonon (sp–ph) coupling is modeled by exact solution up to N = 18 spins. Spin correlation alters the relation between TSP and the singlet–triplet gap, EST, from the free-fermion or mean-field (MF) result by 30%. Direct solution accounts for the transition, spin susceptibility and magnetization of a well-characterized chain of tetrathiafulvalene cation radicals. Strong sp–ph coupling is required for size convergence. Exact analysis conserves total spin, S, while only Sz is conserved in approximate treatments of spinless fermions in infinite chains.