Strong Hilbert space fragmentation via emergent quantum drums in two dimensions

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 rare 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 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. We study two
quasi-one-dimensional
 drums numerically, dubbed ``wire'' and a ``junction of two wires'' respectively.We
find
 that these drums 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 boundaries, a
paradigmatic
 model for quantum many-body scarring; while the junction of two wires represents a
distinct
 constrained model.

 Ref: Anwesha Chattopadhyay, Bhaskar Mukherjee, K. Sengupta, Arnab Sen, SciPost
Phys. 14, 146 (2023)