Distinction Between Transport and R\'enyi Entropy Growth in Kinetically Constrained Models

Understand

Conservation laws and the associated hydrodynamic modes have important consequences on the growth of higher R\'enyi entropies in isolated quantum systems.

• It has been shown in various random unitary circuits and Hamiltonian systems that the dynamics of the R\'enyi entropies in the presence of a U(1) symmetry obey $S^{(n\geq 2)}(t) \propto t^{1/z}$, where $z$ is identified as the dynamical exponent characterizing transport of the conserved charges.
• Here, however, we demonstrate that this simple identification may not hold in certain quantum systems with kinetic constraints.
• In particular, we study two types of U(1)-symmetric quantum automaton circuits with XNOR and Fredkin constraints, respectively.