Dynamics in topological phases with constrained Hilbert spaces

Many topological phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described at low energies by gauge theories with constrained Hilbert spaces. In this talk, I will discuss the steady states of such systems under their own quantum dynamics.
I will first show that a constrained Hilbert space admits a notion of locality and thus adapt the eigenstate thermalization hypothesis (ETH) to this setting. I will then provide numerical evidence in favor of ETH in pinned non-Abelian anyon chains. In the second half of the talk, I will turn to the interplay of spatially random couplings and local constraints.
We will find that constraints stabilize localization at strong randomness in different regimes: remarkably, even when the random couplings do not commute with the local constraints. I will discuss the structure of the accompanying quasi-local integrals of motion and the consequences for near-term quench experiments in Rydberg atomic chains that simulate constrained Ising dynamics.