Related papers: Temperature dependence in Krylov space

Temperature dependence in Krylov space

URL: http://arxiv.org/abs/2508.19233v1
Date: Tue, 26 Aug 2025 17:53:49 GMT
Title: Temperature dependence in Krylov space
Authors: Nikolaos Angelinos, Debarghya Chakraborty, Anatoly Dymarsky,
Abstract summary: We show that the temperature dependence of the corresponding Lanczos coefficients is governed by integrable dynamics.<n>We also discuss the behavior of Lanczos coefficients when the temperature is low but not much smaller than the spectral gap.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We consider the recursion method applied to a generic 2pt function of a quantum system and show, in full generality, that the temperature dependence of the corresponding Lanczos coefficients is governed by integrable dynamics. After an appropriate change of variables, Lanczos coefficients with even and odd indices are described by two independent Toda chains, related at the level of the initial conditions. Consistency of the resulting equations can be used to show that certain scale-invariant models necessarily have a degenerate spectrum. We dub this self-consistency-based approach the ''Krylov bootstrap''. The known analytic behavior of the Toda chain at late times translates into analytic control over the 2pt function and Krylov complexity at very low temperatures. We also discuss the behavior of Lanczos coefficients when the temperature is low but not much smaller than the spectral gap, and elucidate the origin of the staggering behavior of Lanczos coefficients in this regime.

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