Marko Ljubotina: Cages and Collective Bound States in Constrained models

Kinetically constrained models, originally developed to describe slow relaxation in glassy systems, have recently attracted attention in their quantum versions, which feature highly degenerate zero-energy states (zero modes) due to chiral symmetry. Despite this, the structure and implications of these zero modes are not fully understood. This work explores the properties of the zero mode subspace in quantum kinetically constrained models with U(1) particle-conservation symmetry. We show that constraints combined with chiral symmetry lead to a significant increase in zero modes through fragmentation of the Hilbert space into disconnected sectors. Additionally, we introduce collective bound states, a new type of non-ergodic eigenstate, and establish criteria for their existence. These findings highlight the role of zero modes in ergodicity breaking and suggest new directions for studying transport and other phenomena in these models.