LAUSR

Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth. Focusing on systems with U (1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Rényi  entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q , and is in generic case first linear in time, similarly as for systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto ~ 10 5 qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems. Entanglement is one of the most fascinating quantum properties, being a resource in quantum computation and an obstacle in classical simulations. The author analyses entanglement growth in terms of purity, and verifies the results by introducing a class of random Clifford circuits that conserve magnetization, finding that for systems with diffusive dynamics that entanglement growth differs depending on the dimension as well as between qubits or qutrits.