Confinement, dimensional crossover and topological coupling in quasi one dimensional electronic systems

Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The examples are conducting polymers and spin-Peierls chains. We shall discuss topological aspects of elementary excitations, especially the confinement and the dimensional D crossover. At D > 1 the topological requirements for the combined symmetry originate the spin- or charge- roton like excitations with charge- or spin- kinks localized in the core. In quasi 1D world they can be viewed as resulting from a spin-charge recombination due to the 2D or 3D confinement.