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Generalized Krylov Complexity
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Generalized Krylov Complexity
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We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the complexity of states associated with continuous symmetries within a model. Furthermore, we investigate scenarios where different directions of transformation lead to varying degrees of complexity, which can be compared to geometric approaches to understanding complexity, such as Nielsen complexity. In this context, we introduce a generalized orthogonalization algorithm and delineate its computational framework, which is structured as a network of orthogonal blocks rather than a simple linear chain. Additionally, we provide explicit evaluations of specific illustrative examples to demonstrate the practical application of this framework.
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Cited by 1 Pith paper
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Krylov-Space Memory Cores
Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.
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