Entanglement growth in diffusive systems

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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 Renyi 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 generic 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.