Deformed Symmetry Structures and Quantum Many-body Scar Subspaces

2021 
A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is required to have at least a U(1) sub-Lie-group symmetry to allow coherent periodic dynamics from special low-entangled initial states. Based on the sub-group symmetry requirement, we enumerate several possible forms of deforming transformations and recover many existing models whose scar states are not connected by any symmetry. In particular, a two-dimensional scar model is proposed which hosts a periodic dynamical trajectory on which all states are topologically ordered.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    2
    References
    2
    Citations
    NaN
    KQI
    []