  We propose a height-conserving quantum dimer model (hQDM) such that the
lattice sum of its associated height field is conserved, and that it admits a
Rokhsar-Kivelson (RK) point. The hQDM with minimal interaction range on the
square lattice exhibits Hilbert space fragmentation and maps exactly to the XXZ
spin model on the square lattice in certain Krylov subspaces. We obtain the
ground-state phase diagram of hQDM via quantum Monte Carlo simulations, and
demonstrate that a large portion of it is within the Krylov subspaces which
admit the exact mapping to the XXZ model, with dimer ordered phases
corresponding to easy-axis and easy-plane spin orders. At the RK point, the
apparent dynamical exponents obtained from the single mode approximation and
the height correlation function show drastically different behavior across the
Krylov subspaces, exemplifying Hilbert space fragmentation and emergent glassy
phenomena.
