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