Dynamical Solitons and Boson Fractionalization in Cold-Atom Topological Insulators

We study the ${\mathbb{Z}}_{2}$ Bose-Hubbard model, a chain of interacting bosons the tunneling of which is dressed by a dynamical ${\mathbb{Z}}_{2}$ field. The interplay between spontaneous symmetry breaking (SSB) and topological symmetry protection gives rise to interesting fractional topological phenomena when the system is doped to certain incommensurate fillings. In particular, we hereby show how topological defects in the ${\mathbb{Z}}_{2}$ field can appear in the ground state, connecting different SSB sectors. These defects are dynamical and can travel through the lattice carrying both a topological charge and a fractional particle number. In the hardcore limit, this phenomenon can be understood through a bulk-defect correspondence. Using a pumping argument, we show that it survives also for finite interactions, demonstrating how boson fractionalization induced by topological defects can occur in strongly correlated bosonic systems. Our results indicate the possibility of observing this phenomenon, which appears for fermionic matter in solid-state and high-energy physics, using ultracold atomic systems.