Fragmentation and glassy dynamics in frustrated spin models with kinematic constraints

Constrained dynamics due to frustration can give rise to glassy behavior in many-body systems. Typical quantum many-body systems thermalize on short time scales independent of the initial condition. However, recent developments show that a large class of systems either do not thermalize or relax anomalously slow for certain initial states, falling outside the rubric of eigenstate thermalization hypothesis. In clean systems, kinematic constraints can lead to Hilbert space fragmentations where certain states fail to reach the thermal steady state. We show that such fragmentation naturally arises in frustrated magnets with low-energy “ice manifolds,” which give rise to a broad range of relaxation time scales. Focusing on kagome lattice, we explicitly show the fragmentation in the Balents-Fisher-Girvin Hamiltonian and a three-coloring model with loop excitations, both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of glassiness in various limits of the XXZ model on the kagome lattice.