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.