Hilbert space fragmentation and exact scars of generalized Fredkin spin chains

In this work, based on the Fredkin spin chain, we introduce a family of spin-1/2 many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved s...

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Bibliographic Details
Published in:Physical review. B 2021-06, Vol.103 (22), p.1, Article L220304
Main Authors: Langlett, Christopher M., Xu, Shenglong
Format: Article
Language:English
Subjects:
Chains
Eigenvectors
Entanglement
Fragmentation
Hilbert space
Scars
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Summary:In this work, based on the Fredkin spin chain, we introduce a family of spin-1/2 many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the one-dimensional Fermi-Hubbard model in the infinite on-site repulsion limit. To demonstrate the many-body scars, we construct an exact middle spectrum eigenstate within each fractured subsector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable nonergodic dynamics by quenching different initial states shown through large-scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays nonergodic dynamics due to sharing the same fragmentation structure and scarring as the Hamiltonian.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.103.L220304