Numerical methods for detecting symmetries and commutant algebras

Utilizing the understanding of symmetries in framework commutant algebras, authors introduce here general methods to numerically construct symmetry operators and quantum number sectors. One method uses simultaneous block diagonalization two generic Hamiltonians sectors, while another fact that are frustration-free ground states local superoperators, which leads efficient algorithms. These applied conventional on-site symmetries, as well unconventional such Hilbert space fragmentation many-body scars.