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.
Highlights
The experimental discovery of slow thermalization dynamics in the Rydberg atom array [1–3], which is later formulated as a theoretical PXP model [4–15], has since stimulated the study of a novel kind of weakly ergodicity breaking phenomenon, later known as the quantum many-body scar (QMBS)
We proposed a deformed symmetry framework to describe a large class of exact scar space in quantum many-body scar models
A general scar space can be generated from two inputs: (i) a prototype symmetric space and (ii) a deforming transformation realized by finite-dimensional matrix-product operator (MPO) and PEPO
Summary
The experimental discovery of slow thermalization dynamics in the Rydberg atom array [1–3], which is later formulated as a theoretical PXP model [4–15], has since stimulated the study of a novel kind of weakly ergodicity breaking phenomenon, later known as the quantum many-body scar (QMBS) (see Refs. [16,17] for reviews). Under which Hscar is strictly decoupled, and the spaced energy implies revival dynamics within Hscar [46,47] While it unifies several known exact scar models, the quasisymmetry framework still misses a number of cases. There are models whose scar spaces have no quasisymmetry structure (for example, the AKLT model) and models having reducible symmetry sectors as their scar spaces [for example, the Rydberg-antiblockaded model, whose scar space has U(1) quasisymmetry], in which case the degeneracies in Hq lack a theoretical understanding To address these drawbacks, in this work, we extend the previous symmetry-based theoretical framework by formulating the scar space as the deformed symmetry sector, which is an irreducible sector of a simple Lie group G0 acted by a transformation Tpreserving the nonthermal entanglement of the scar states.
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