Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Entanglement entropies of an interval in the free Schr¨ odinger field theory on the half line,
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Holographic Krylov Complexity with Lifshitz Scaling and Hyperscaling Violation
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.