Krylov complexity from integrability to chaos
Krylov complexity from integrability to chaos
We apply a notion of quantum complexity, called “Krylov complexity”, to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking deformation that allows one to interpolate between integrable and chaotic behavior. K-complexity can act as a probe of the integrable or chaotic nature of the underlying system via its late-time saturation value that is suppressed in the integrable phase and increases as the system is driven to the chaotic phase. We furthermore ascribe the (under-)saturation of the late-time bound to the amount of disorder present in the Lanczos sequence, by mapping the complexity evolution to an auxiliary off-diagonal Anderson hopping model. We compare the late-time saturation of K-complexity in the chaotic phase with that of random matrix ensembles and find that the chaotic system indeed approaches the RMT behavior in the appropriate symmetry class. We investigate the dependence of the results on the two key ingredients of K-complexity: the dynamics of the Hamiltonian and the character of the operator whose time dependence is followed.
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, Ruth
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
26 July 2022
Rabinovici, E.
f97c4550-c0ad-4837-a529-42387151ea9d
Sánchez-Garrido, A.
6add42c4-992e-455c-a098-f26e85168537
Shir, Ruth
80e05c9b-9440-4c4d-a5b8-95cebfaa32f3
Sonner, J.
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
Rabinovici, E., Sánchez-Garrido, A., Shir, Ruth and Sonner, J.
(2022)
Krylov complexity from integrability to chaos.
JHEP, 2022, [151].
(doi:10.1007/JHEP07(2022)151).
Abstract
We apply a notion of quantum complexity, called “Krylov complexity”, to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking deformation that allows one to interpolate between integrable and chaotic behavior. K-complexity can act as a probe of the integrable or chaotic nature of the underlying system via its late-time saturation value that is suppressed in the integrable phase and increases as the system is driven to the chaotic phase. We furthermore ascribe the (under-)saturation of the late-time bound to the amount of disorder present in the Lanczos sequence, by mapping the complexity evolution to an auxiliary off-diagonal Anderson hopping model. We compare the late-time saturation of K-complexity in the chaotic phase with that of random matrix ensembles and find that the chaotic system indeed approaches the RMT behavior in the appropriate symmetry class. We investigate the dependence of the results on the two key ingredients of K-complexity: the dynamics of the Hamiltonian and the character of the operator whose time dependence is followed.
Text
JHEP07(2022)151
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Accepted/In Press date: 17 July 2022
Published date: 26 July 2022
Identifiers
Local EPrints ID: 501040
URI: http://eprints.soton.ac.uk/id/eprint/501040
ISSN: 1126-6708
PURE UUID: fb733a19-9f35-4863-ae2c-06a724dd8e8e
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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:
Ruth Shir
Author:
J. Sonner
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