Soliton lattice in polyacetylene, spin-peierls systems, and two-dimensional sine-gordon systems

An exact solution for the soliton lattice in the half-filled-band Peierls condensate is found. In the limit of weak coupling (infinite momentum cutoff ) the soliton-soliton interaction decays as a repulsive exponential while for finite it decays as (distance)-1 and is attractive! This yields phase separation in doped polyacetylene or a first-order lock-in transition of a spin-Peierls system. A mapping into the low-temperature two-dimensional sine-Gordon system is shown, where a lock-in transition has exponent =1 for finite .