We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice.The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment.We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space.Given any product NEFF U1ACE2HN0B Electric Double Oven - Stainless Steel state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums".
These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum.The spectra of some small drums is calculated analytically.We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively.We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states.
The wire is shown to be equivalent to the one-dimensional PXP chain with open Magnetic Contact Switch boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.