Topological Excitations of One-Dimensional Correlated Electron Systems

TL;DR

This paper explores the topological nature of low-energy excitations in one-dimensional correlated electron systems, introducing a winding number as a new measurable attribute that characterizes these excitations beyond conventional quantum numbers.

Contribution

It introduces a novel topological quantum number, the winding number, to describe elementary excitations in 1D correlated systems, expanding understanding of their properties.

Findings

Winding number distinguishes neutral spin-1/2 excitations from electrons and holes.

Topological excitations can have irrational winding numbers if charge is irrational.

Excitations are composite particles dressed by order parameter kinks.

Abstract

Properties of low-energy excitations in one-dimensional superconductors and density-wave systems are examined by the bosonization technique. In addition to the usual spin and charge quantum numbers, a new, independently measurable attribute is introduced to describe elementary, low-energy excitations. It can be defined as a number w which determines, in multiple of $\pi$, 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 for neutral spin-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, and they can be viewed as composite particles made of spin or charge degrees of freedom and dressed by kinks in the order parameter.