Fragmented Hilbert Spaces and Slow Dynamics in Quantum Dimer Models

The presence of dynamical constraints can have severe impacts on the non-equilibrium dynamics of closed quantum systems, leading to slow or even non-ergodic behavior at finite energy densities. One mechanism for the occurrence of such features is a fragmentation of the Hilbert space structure in systems of fractons, consisting of particles with reduced mobility [1]. Within this context, we investigate the connectivity of configuration spaces resulting from the hard core constraint in close-packed dimer models. On the square lattice, we uncover the emergence of effectively immobile defects within a staggered background, whose dynamics is impeded up to high orders in perturbation theory. This fracton-like structure of the low energy Hilbert space is shown to give rise to glassy behavior for states at low temperatures [2]. We further discuss extensions to different lattices and dimensions that allow for the explicit construction of large sets of conserved quantities, leading to slow dynamics and localized modes for typical states also at high energies.

[1] P. Sala, T. Rakovszky, R. Verresen, M. Knap, F. Pollmann, arXiv:1904.04266 (2019)
[2] J. Feldmeier, F. Pollmann, M. Knap, PRL 123, 040601 (2019)