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 $U\left(1\right)$ 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 $U\left(1\right)$ 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.

Program summary

Program title: ResEE.jl

CPC Library link to program files: https://doi.org/10.17632/d8s5byx96r.1

Developer's repository link: https://github.com/top2group/ResEE.jl

Licensing provisions: MIT License

Programming language: Julia

Nature of problem: Computing the entanglement entropy of quantum many-body systems with restricted Hilbert space and/or $U\left(1\right)$ symmetry.

Solution method: The program constructs a map table to efficiently compute the reduced density matrix in systems with restricted Hilbert spaces. For $U\left(1\right)$ symmetric systems, it exploits charge conservation to put the reduced density matrix in a block-diagonal form, further improving the efficiency.