Bull, K, Desaules, J-Y and Papic, Z orcid.org/0000-0002-8451-2235 (2020) Quantum scars as embeddings of weakly broken Lie algebra representations. Physical Review B: Condensed Matter and Materials Physics, 101 (16). 165139. ISSN 1098-0121
Abstract
Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium. An example of such nonthermalizing behavior is the phenomenon of quantum many-body scars, which has been experimentally observed in Rydberg-atom quantum simulators. Here, the authors show that many-body scars can generally be viewed as forming approximate subspaces of “broken” Lie algebra representations. Furthermore, they use an iterative process to identify perturbations which “correct” the broken Lie algebra, resulting in improved quantum revivals from special initial states. The description of embedded Lie algebra representations unifies several theoretical models, which feature exact many-body scars, with experimentally realized models, such as the constrained Rydberg-atom system, where scars only form an approximate Lie algebra representation.
We present an interpretation of scar states and quantum revivals as weakly “broken” representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly interacting Rydberg atoms, supports a “loose” embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn〉, including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2020 American Physical Society. This is an author produced version of a paper published in Physical Review B: covering condensed matter and materials physics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Theoretical Physics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/R020612/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Apr 2020 14:49 |
Last Modified: | 29 Apr 2020 14:49 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevB.101.165139 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159971 |