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Operator growth and Krylov construction in dissipative open quantum systems

Bhattacharya, A and Nandy, P and Nath, PP and Sahu, H (2022) Operator growth and Krylov construction in dissipative open quantum systems. In: Journal of High Energy Physics, 2022 (12).

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Official URL: https://doi.org/10.1007/JHEP12(2022)081


Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems. © 2022, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to Springer.
Keywords: Field Theories in Lower Dimensions; Holography and Condensed Matter Physics (AdS/CMT); Integrable Field Theories
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 25 Jan 2023 06:26
Last Modified: 25 Jan 2023 06:26
URI: https://eprints.iisc.ac.in/id/eprint/79491

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