Robust Topological Order in Fermionic Z2 Gauge Theories: From Aharonov-Bohm Instability to Soliton-Induced Deconfinement

Abstract

Topologically ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Thus, their preparation requires 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 Z2 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. Moreover, the latter coexists here with a symmetry-protected topological phase in the matter sector, which displays fractionalized gauge-matter edge states and intertwines with it by a flux-threading phenomenon. Finally, we unveil the robustness of these features through a gauge frustration mechanism, akin to geometric frustration in spin liquids, allowing topological order to survive to arbitrarily large quantum fluctuations. In particular, we show how, at finite chemical potential, topological solitons are created in the gauge field configuration, which bound to fermions and form Z2 deconfined quasiparticles. The simplicity of the model makes it an ideal candidate for 2D gauge theory phenomena, as well as exotic topological effects, to be investigated using cold-atom quantum simulators.