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.

Automated summary

In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. Coupling an external field to certain generators of the quasisymmetry group can lift the degeneracy and result in exactly periodic dynamics within the degenerate subspace.