Geometry of Noisy Quantum Many-Body Dynamics with Continuous Symmetries: Entanglement and Correlations

• URL: http://arxiv.org/abs/2608.11297v1
• Date: Tue, 11 Aug 2026 18:00:01 GMT
• Title: Geometry of Noisy Quantum Many-Body Dynamics with Continuous Symmetries: Entanglement and Correlations
• Abstract summary: We study unitary quantum dynamics in noisy Brownian models with global continuous symmetries.<n>This work focuses on Rényi entanglement entropies and hydrodynamic and non-hydrodynamic correlators.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study unitary quantum dynamics in noisy Brownian models with global continuous symmetries, such as $U(1)$ and $SU(2)$, focusing on Rényi entanglement entropies and hydrodynamic and non-hydrodynamic correlators. By mapping the averaged late-time dynamics to the low-energy physics of effective replica Hamiltonians, we find that the evolution is controlled by the quantum geometry of their ground-state manifolds, which is directly related to the geometry of $k$-commutants---the symmetry algebra of $k$ replicas of the system. In interacting systems, these $k$-commutants are generically determined solely by the symmetries of the system, independent of microscopic details of the noisy evolution. This allows us to use the time-dependent variational principle (TDVP) to provide simple geometric explanations for the sub-ballistic Rényi entanglement growth and the anomalous decay of non-hydrodynamic correlators in interacting systems with continuous symmetries. We find this behavior to be intimately connected to singularities within the $k$-commutant manifolds, arising from frozen ``void'' states in the Hilbert space that exist due to continuous on-site symmetries. This also demystifies the important role of voids in the dynamics of these observables, previously identified in $U(1)$ symmetric systems. We compare these behaviors in interacting systems with Abelian and non-Abelian continuous symmetries and in free-fermion systems, which differ in the geometry of their $k$-commutants. Ultimately, this work provides a general geometric framework for systematically studying observables in noisy systems with continuous symmetries, including Haar-random circuits.

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