A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry

TL;DR

This paper introduces a novel glide reflection symmetric two-leg SSH model realized with ultracold atoms, revealing new topological phenomena such as non-abelian Berry phases and charge fractionalization.

Contribution

It proposes a new glided-two-leg SSH model using ultracold atoms that exhibits unique topological properties beyond traditional SSH models.

Findings

Presence of non-abelian Berry connections in the model

Charge fractionalization without lattice interfaces

Interplay of glide symmetry and interactions leads to novel phenomena

Abstract

The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important concepts in quantum topological matters. Since it tells one that topological states may be distinguished by abelian geometric phases, a question naturally arises as to what happens if one assembles two topologically distinct states. Here, we show that a spin-dependent double-well optical lattice allows one to couple two topologically distinct SSH chains in the bulk and realise a glided-two-leg SSH model that respects the glide reflection symmetry. Such model gives rise to intriguing quantum phenomena beyond the paradigm of a traditional SSH model. It is characterised by Wilson line that requires non-abelian Berry connections, and the interplay between the glide symmetry and interaction automatically leads to charge fractionalisation without jointing two lattice potentials at an interface. Our work demonstrates the power of ultracold atoms to create new theoretical models for studying topological matters.