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arXiv:2610.23781

Transport and thermalization under noncommuting localized constraints

Amir Nesturov, Attila Takács, Lenart Zadnik

cond-mat.stat-mechquant-phSubmitted Oct 16, 2026• Announced Oct 19, 2026• 0 citations
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Abstract

We investigate the effects of spatially localized conserved quantities on transport and thermalization in quantum and classical many-body systems. We consider several related models: the integrable quantum Volterra model, its nonintegrable classical limit, and two cellular automata derived from the latter. Although localized constraints are often associated with lattice gauge theories, our models do not admit such an interpretation. In systems with discrete degrees of freedom, these constraints induce uniform fragmentation of the Hilbert or configuration space. In the quantum Volterra model, we derive an exact mapping of the dynamics within each Hilbert-space fragment onto a quantum chiral Potts chain. We find that energy transport is ballistic, with identical transport coefficients across all fragments. In the nonintegrable classical limit, energy transport is diffusive, and we similarly find the diffusion constant to be independent of whether or not the constraints are fixed (resolved). Finally, in the cellular automata, we show that, despite leaving transport unaffected, localized constraints lead to a strong breakdown of local ergodicity.

Comments
12 pages, 4 figures

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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 —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 U ( 1 ) particle-conservation symmetry. We use the U ( 1 ) East, which lacks inversion symmetry, and the inversion-symmetric U ( 1 ) 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 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 , a special kind of nonergodic 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 U ( 1 ) 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.