Krylov Complexity Under Hamiltonian Deformations and Toda Flows

• URL: http://arxiv.org/abs/2510.19436v1
• Date: Wed, 22 Oct 2025 10:02:03 GMT
• Title: Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Authors: Kazutaka Takahashi, Pratik Nandy, Adolfo del Campo,
• Abstract summary: We apply the Krylov subspace method for Hamiltonian deformations.<n>We relate the evolution of deformed and undeformed theories.<n>We observe time evolutions with a reorganized basis.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of constructing solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace is unchanged, and we observe time evolutions with a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.

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