Topological phases in odd-legs frustrated synthetic ladders

TL;DR

This paper demonstrates that Hofstadter models in odd-leg synthetic ladder geometries exhibit unique topological phases with protected edge states, distinct from two-dimensional systems, and applicable in cold atom experiments.

Contribution

It reveals a new topological phase in odd-leg ladder systems derived from Hofstadter Hamiltonian, protected by inversion symmetry, and extends the analysis to ladders with more legs.

Findings

Presence of robust fermionic edge modes in three-leg ladders

Degenerate entanglement spectrum indicating topological order

Non-zero Zak phase confirming topological nature

Abstract

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry, and is protected by a properly defined inversion symmetry. We start our analysis considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum and a non-zero Zak phase; then, we generalize our findings - addressable in the state-of-the-art cold atom experiments - to ladders with an higher number of legs.