paper

Fragmentation, Zero Modes, and Collective Bound States in Constrained Models

arXiv:2504.17627 · doi:10.1103/sl79-1xgb

Abstract

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy -- known as zero modes -- stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a particle-conservation symmetry. We use the East, which lacks inversion symmetry, and the inversion-symmetric East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single particle physics and introduce the notion of collective bound states, a special kind of non-ergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the North-East, and in the pair-flip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.

21 pages, 12 figures, accepted version

References in corpus (56)

Cited by in corpus (2)