Fig. 1: HSF and schematic of the experiment.
From: Observation of Hilbert space fragmentation and fractonic excitations in 2D
a, The Hilbert space consists of sectors with fixed energy and particle number (conserved quantities), (E, N) (grey squares). Adding dynamical constraints to the system, these sectors fragment into decoupled Krylov subsectors (pink squares). b, Our system is described by a tilted Bose–Hubbard model with a diagonal tilt (realized using a magnetic field B) along the x + y direction tuned to resonance with the interactions, Δ = U. Tilt and interaction energy are much larger than the tunnel coupling J. c, Dimer (blue points, bottom left) and chequerboard state (orange points, top right) and first-order processes exemplifying the presence (absence) of density-assisted resonant couplings in the lattice for the dimer (chequerboard) state.
