Geometric fragmentation and anomalous thermalization in cubic dimer model

Abstract: While quantum statistical mechanics triumphs in explaining many equilibrium phenomena, there is an increasing focus on going beyond conventional scenarios of thermalization. Traditionally examples of non-thermalizing systems are either integrable, or disordered. Recently, examples of translationally-invariant physical systems have been discovered whose excited energies avoid thermalization either due to local constraints (whether exact or emergent), or due to higher-form symmetries. In this article, we extend these investigations for the case of 3D $U(1)$ quantum dimer models, which are lattice gauge theories with finite-dimensional local Hilbert spaces (also generically called quantum link models) with staggered charged static matter. Using a combination of analytical and numerical methods, we uncover a class of athermal states that arise in large winding sectors, when the system is subjected to external electric fields. The polarization of the dynamical fluxes in the direction of applied field traps excitations in 2D planes, while an interplay with the Gauss Law constraint in the perpendicular direction causes exotic athermal behaviour due to the emergence of new conserved quantities. This causes a geometric fragmentation of the system. We provide analytical arguments showing that the scaling of the number of fragments is exponential in the linear system size, leading to weak fragmentation. Further, we identify sectors which host fractonic excitations with severe mobility restrictions. The unitary evolution of fragments dominated by fractons is qualitatively different from the one dominated by non-fractonic excitations.