Robust topological order in fermionic $\mathbb{Z}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement

Understand

Topologically-ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams.

• Their preparation requires thus a precise fine tunning of the system's parameters, a very challenging task in most experimental setups.
• In this work, we investigate a model of spinless fermions interacting with dynamical $\mathbb{Z}_2$ gauge fields on a cross-linked ladder, and show evidence of topological order throughout the full parameter space.
• In particular, we show how a magnetic flux is spontaneously generated through the ladder due to an Aharonov-Bohm instability, giving rise to topological order even in the absence of a plaquette term.