Quasisymmetry Groups and Many-Body Scar Dynamics

In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those itself. When this enhanced-symmetry group can be generated from local operators, we call it quasisymmetry group. is Lie group, an external field coupled to certain generators lifts degeneracy, and results in exactly periodic dynamics within subspace, namely, many-body-scar (given that nonintegrable). We provide two related schemes for constructing one-dimensional spin models having on-demand groups, with exact evolution prechosen product or matrix-product state under fields.