Krylov Localization and suppression of complexity
- URL: http://arxiv.org/abs/2112.12128v2
- Date: Sat, 2 Apr 2022 18:49:51 GMT
- Title: Krylov Localization and suppression of complexity
- Authors: E. Rabinovici, A. S\'anchez-Garrido, R. Shir and J. Sonner
- Abstract summary: We investigate Krylov complexity for the case of interacting integrable models at finite size.
We find that complexity saturation is suppressed as compared to chaotic systems.
We demonstrate this behavior for an interacting integrable model, the XXZ spin chain.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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