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Probing quantum scars and weak ergodicity breaking through quantum complexity

Bhattacharjee, B and Sur, S and Nandy, P (2022) Probing quantum scars and weak ergodicity breaking through quantum complexity. In: Physical Review B, 106 (20).

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Official URL: https://doi.org/10.1103/PhysRevB.106.205150


Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Néel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such “closeness” by the q -deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Néel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Néel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Approximation algorithms; Forward scattering; Quantum theory, Breakings; Eigenstates; Ergodicity; Lanczos; Lanczos algorithm; Many body; Quantum complexity; Scattering approximation; Thermalization; Time evolutions, Hamiltonians
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 18 Jan 2023 05:05
Last Modified: 18 Jan 2023 05:05
URI: https://eprints.iisc.ac.in/id/eprint/79196

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