Data and code for "Coherence dynamics in quantum many-body systems with conservation laws"

We investigate how conservation laws govern the spreading of quantum coherence in many-body systems, studying U(1)-symmetric random circuits, circuits conserving both charge and dipole moment, and ergodic Hamiltonian dynamics. We characterize coherence globally through the participation entropy and locally through the relative entropy of coherence. Combining exact state-vector evolution, matrix product state simulations, and replica tensor network methods, we find that conservation laws replace the logarithmic saturation times of unconstrained circuits with slow hydrodynamic relaxation of global coherence. Locally, symmetry-constrained circuits exhibit a pronounced rise, peak, and decay, with a peak time that grows algebraically with subsystem size. In ergodic Hamiltonian dynamics, the peak instead broadens into an extended plateau for larger subsystems, revealing a distinct pattern of coherence relaxation. These results establish coherence as a sensitive probe of symmetry-constrained thermalization and connect quantum resource dynamics to many-body transport.