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 $\Lambda$) the soliton-soliton interaction decays as a repulsive exponential while for finite $\Lambda$ it decays as ${\mathrm{}\left(\mathrm{distance}\right)\mathrm{}}^{-1\mathrm{}}$ 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 $\beta =1\mathrm{}$ for finite $\Lambda$.