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.