A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension

TL;DR

This paper demonstrates the existence of a gapless, symmetry-protected topological phase in a one-dimensional fermionic system with interactions and spin-orbit coupling, featuring localized edge states despite bulk gaplessness.

Contribution

It introduces a new gapless topological phase in 1D fermionic systems with spin-orbit coupling, supported by analytical and numerical evidence.

Findings

Existence of a topological phase with protected edge states in a gapless system

Analytical and DMRG numerical validation of the phase

Edge state localization due to spin gap or bulk single-particle gap

Abstract

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show that a sharply defined topological phase with protected, exponentially localized edge states exists. If one of the spin components is conserved, the protection of the edge modes can be understood as a consequence of the presence of a spin gap. In the more general case, the localization of the edge states arises from a gap to single particle excitations in the bulk. We consider specific microscopic models and demonstrate both analytically and numerically (using density matrix renormalization group calculations) that they can support the topologically non-trivial phase.