Title: Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems

Abstract: The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm due to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which thermalisation can be strongly suppressed. Here, we experimentally observe Hilbert space fragmentation (HSF) in a two-dimensional tilted Bose-Hubbard model. Using quantum gas microscopy, we engineer a wide variety of initial states and find a rich set of manifestations of HSF involving bulk states, interfaces and defects, i.e., d = 2, 1 and 0 dimensional objects. Specifically, uniform initial states with equal particle number and energy differ strikingly in their relaxation dynamics. Inserting controlled defects on top of a global, non-thermalising chequerboard state, we observe highly anisotropic, sub-dimensional dynamics, an immediate signature of their fractonic nature. An interface between localized and thermalising states in turn displays dynamics depending on its orientation. Our results mark the first observation of HSF beyond one dimension, as well as the concomitant direct observation of fractons, and pave the way for in-depth studies of microscopic transport phenomena in constrained systems