An efficient algorithm for computing entanglement entropy in systems with a restricted Hilbert space or U(1) symmetry

We present an efficient algorithm for computing entanglement entropies in systems with a restricted Hilbert space or U(1) symmetry. For the case of a restricted Hilbert space, the algorithm is straightforward in that only a map table from physical states to indices of an intermediate matrix is needed. In systems with a U(1) symmetry, the reduced density matrix can be put into a block-diagonal form by properly grouping matrix elements according to the total charge in the subsystem, leading to a significant boost in the efficiency of entanglement entropy calculation.我们提出了一种高效算法，用于计算受限希尔伯特空间（restricted Hilbert space）或具有U(1)对称性（U(1) symmetry）的系统中的纠缠熵（entanglement entropy）。针对受限希尔伯特空间的场景，该算法简洁直观，仅需一张将物理态映射至中间矩阵索引的映射表即可。对于具有U(1)对称性的系统，通过依据子系统的总电荷对矩阵元进行合理分组，可将约化密度矩阵（reduced density matrix）转化为分块对角形式，从而显著提升纠缠熵的计算效率。