Symmetry protected topological Luttinger liquids and the phase transition between them

TL;DR

This paper demonstrates that doped spin-1/2 ladders can host symmetry protected topologically non-trivial Luttinger liquids, with phase transitions driven by spin anisotropy, revealing novel boundary excitations and pairing symmetries.

Contribution

It introduces a new class of topologically non-trivial Luttinger liquids in doped spin ladders and characterizes the phase transition driven by spin anisotropy.

Findings

Identification of a topologically non-trivial Luttinger liquid phase.

Observation of a phase transition with spin gap closing.

Different Cooper pair symmetries in trivial and non-trivial phases.

Abstract

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet $d_{xy}$ in the non-trivial phase and triplet $S_z=0$ in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.