Frustration-induced Emergent Hilbert Space Fragmentation

Frustration in interacting systems can constrain dynamics which in turn gives rise to glassy behavior. Although interacting quantum systems tend to thermalize locally on short time scales independent of initial conditions, recent developments have shown that this can be avoided for a large class of disordered and clean systems where the system either fails to thermalize or takes an anomalously long time for certain initial states to do so. These phenomena are understood as falling outside the rubric of the eigenstate thermalization hypothesis. For clean systems the constraints can lead to fragmentations of Hilbert space where certain initial states fail to reach the thermal steady state. We show that such fragmentation naturally arises in many frustrated magnets with low-energy "ice manifolds" which gives rise to a broad range of relaxation times for different initial states. Focusing our attention to the kagome lattice, we explicitly show the phenomenology of fragmentation in the Balents-Fisher-Girvin Hamiltonian relevant to the easy-axis (Ising) regime, and a three-coloring model with loop excitations relevant to the easy-plane (XY) regime, both with constrained Hilbert spaces. We study their level statistics, and initial state dependence of relaxation dynamics to develop a coherent picture of glassiness in various limits of the XXZ model on the kagome lattice