Topological Excitations of One-Dimensional Correlated Electron Systems

Elementary, low-energy excitations are examined by bosonization in one-dimensional systems with quasi-long-range order. A new, independently measurable attribute is introduced to describe such excitations. It is defined as a number $w$ which determines how many times the phase of the order parameter winds as an excitation is transposed from far left to far right. The winding number is zero for electrons and holes with conventional quantum numbers, but it acquires a nontrivial value $w=1\mathrm{}$ for neutral spin- $\frac{1}{2}$ excitations and for spinless excitations with a unit electron charge. It may even be irrational, if the charge is irrational. Thus, these excitations are topological.