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 ~ 10⁵ qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems.

纠缠有助于理解各种现象，从量化复杂性到对物质阶段进行分类。在这里，我们研究了守恒定律对纠缠增长的影响。着眼于具有U（1）对称性的系统，即表现出扩散动力学的电荷或磁化守恒，我们从理论上预测了由Rényi熵量化的纠缠的增长，在任何空间维数d以及任何局部维的晶格系统中希尔伯特空间维数q（qudits）。我们发现增长取决于d和q，并且在一般情况下，时间首先是线性的，类似于没有任何守恒定律的系统。该规则的例外是2级系统链，其中依赖性始终是时间的平方根。通过对高达约10 ⁵量子位的扩散Clifford电路进行仿真，对预测进行了数值验证。这种有效的可仿真电路应该是解决其他多体问题的有用工具。