Deformed Symmetry Structures and Quantum Many-body Scar Subspaces
- URL: http://arxiv.org/abs/2108.07817v3
- Date: Mon, 29 Nov 2021 07:57:23 GMT
- Title: Deformed Symmetry Structures and Quantum Many-body Scar Subspaces
- Authors: Jie Ren, Chenguang Liang, and Chen Fang
- Abstract summary: A quantum many-body scar system usually contains a special non-thermal subspace decoupled from the rest of the Hilbert space.
We propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars.
- Score: 12.416248333306237
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 certain low-entangled initial states. We enumerate several
possible deforming transformations based on the sub-group symmetry requirement
and recover many existing models whose scar states are not connected by
symmetry. In particular, a two-dimensional scar model is proposed, which hosts
a periodic dynamical trajectory on which all states are topologically ordered.
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