Topological properties of gapless phases in an interacting spinful wire

TL;DR

This paper explores topological gapless phases in an interacting spinful wire, revealing novel boundary states with fractionalized excitations and connecting them to non-interacting topological phases.

Contribution

It identifies and characterizes two topologically non-trivial gapless boundary states in an interacting model, linking them to non-interacting topological phases despite the absence of local order parameters.

Findings

Discovery of topological Luther-Emery liquid with fractional spin edge modes.

Identification of topological Mott insulator with fractional charge edge states.

Connection of interacting gapless phases to non-interacting topological metals.

Abstract

We study topology in gapless phases of an interacting spinful model with spin-charge separation. We focus on the gapless boundaries between $\mathbb{Z}_2$ symmetry-breaking phases. We find two topologically non-trivial gapless states that occur at the boundary between a non-trivial and a trivial insulator. They correspond to topological Luther-Emery liquid and topological Mott insulator. The Luther-Emery liquid is characterized by gapless charge excitations and features topological edge modes that carry fractional spin, while the topological Mott insulator has gapless spin sector and features edge states that carry fractional charge. Surprisingly, even though there is no mean-field description of the interacting gapless phases, as there is no local order parameter, we show that they can be adiabatically connected to a non-interacting topological metal. This non-interacting state is a phase boundary between decoupled Su-Schrieffer-Heeger chains with the winding number $\nu=2$ and chains with $\nu=1$.