D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
Krylov complexity has it all
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This paper establishes that Krylov complexity contains the entire information about the dynamics of a quantum operator, extending the list of equivalent quantities that can serve this purpose, such as the Lanczos coefficients, the return amplitude, and the spectral density. To demonstrate this equivalence, an explicit recursive algorithm is constructed to calculate Lanczos coefficients from the Taylor expansion of the Krylov complexity around $t=0$. Furthermore, the paper discusses the distinction between Krylov and spread complexity, clarifying why a similar recursive algorithm cannot exist for the latter without additional dynamical input. These results provide a ``proof of principle'' for using Krylov complexity as a complete characterization of operator evolution in quantum systems.
fields
hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.
citing papers explorer
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Holographic Spread Complexity from Branes and Strings
D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
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Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity
Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.