Krylov localization and suppression of complexity
Krylov localization and suppression of complexity
Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that localization is enhanced in the integrable case due to a stronger disorder in the hopping amplitudes, inducing an effective suppression of Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define: this model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, R.
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
31 March 2022
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, R.
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
Rabinovici, E., Sánchez-Garrido, A., Shir, R. and Sonner, J.
(2022)
Krylov localization and suppression of complexity.
JHEP, 2022, [211].
(doi:10.1007/JHEP03(2022)211).
Abstract
Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that localization is enhanced in the integrable case due to a stronger disorder in the hopping amplitudes, inducing an effective suppression of Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define: this model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.
Text
JHEP03(2022)211
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Accepted/In Press date: 10 March 2022
Published date: 31 March 2022
Identifiers
Local EPrints ID: 501041
URI: http://eprints.soton.ac.uk/id/eprint/501041
ISSN: 1126-6708
PURE UUID: c44db3b8-ec84-4354-8d07-5b258d9b4203
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Date deposited: 21 May 2025 16:31
Last modified: 22 Aug 2025 02:43
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Author:
E. Rabinovici
Author:
A. Sánchez-Garrido
Author:
R. Shir
Author:
J. Sonner
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