Krylov Distribution

• URL: http://arxiv.org/abs/2602.06150v1
• Date: Thu, 05 Feb 2026 19:39:53 GMT
• Title: Krylov Distribution
• Authors: Mohsen Alishahiha, Mohammad Javad Vasli,
• Abstract summary: The Krylov distribution $mathcalD()$ characterizes how inverse-energy response is organized in Hilbert space.<n>We identify three universal regimes: saturation outside the spectral support, extensive growth within continuous spectra, and sublinear or logarithmic scaling near spectral edges.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the Krylov distribution $\mathcal{D}(ξ)$, a static Krylov-space diagnostic that characterizes how inverse-energy response is organized in Hilbert space. The central object is the resolvent-dressed state $(H-ξ)^{-1}|ψ_0\rangle$, whose decomposition in the Krylov basis generated from a reference state defines a normalized distribution over Krylov levels. Unlike conventional spectral functions, which resolve response solely along the energy axis, the Krylov distribution captures how the resolvent explores the dynamically accessible subspace as the spectral parameter $ξ$ is varied. Using asymptotic analysis, exact results in solvable models, and numerical studies of an interacting spin chain, we identify three universal regimes: saturation outside the spectral support, extensive growth within continuous spectra, and sublinear or logarithmic scaling near spectral edges and quantum critical points. We further show that fidelity susceptibility and the quantum geometric tensor admit natural decompositions in terms of Krylov-resolved resolvent amplitudes.

Related papers

• Krylov Distribution and Universal Convergence of Quantum Fisher Information [0.0]
  We develop a framework for computing the quantum Fisher information computation (QFI) using Krylov subspace methods.<n>By expressing the QFI as a resolvent moment of the superoperator $mathcalK_ universality associated with a density matrix, the Krylov distribution quantifies how the QFI weight is distributed across Krylov levels.
  arXiv  Detail & Related papers  (2026-02-23T11:59:29Z)
• Universality of equilibration dynamics after quantum quenches [0.0]
  We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits universality''<n>We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.
  arXiv  Detail & Related papers  (2025-12-24T18:19:57Z)
• Variations on a Theme of Krylov [1.9116784879310027]
  We show how variations in initial conditions, the Hamiltonian, and the dimension of the Hilbert space affect spread complexity and Krylov basis structure.<n>We then describe a lattice model that displays linear growth of spread complexity, saturating for bounded lattices and continuing forever in a thermodynamic limit.
  arXiv  Detail & Related papers  (2025-11-05T19:00:00Z)
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity [0.0]
  We show that the brickwall model exhibits features consistent with random matrix theory across various ensembles.<n>We also identify signatures of integrability at extreme values of the Dirichlet boundary condition parameter.
  arXiv  Detail & Related papers  (2024-12-16T19:12:59Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Quantum chaos, integrability, and late times in the Krylov basis [0.8287206589886881]
  Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features are well described by Random Matrix Theory (RMT) We show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffices to produce the full long time behavior of general survival probabilities. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos.
  arXiv  Detail & Related papers  (2023-12-06T19:02:22Z)
• Decomposing the Spectral Form Factor [0.0]
  Correlations between energies of a system's spectrum are one of the defining features of quantum chaos.<n>We investigate how each spectral distance contributes in building this two-point correlation function.<n>We show how the onset of the ramp, characterized either by the dip or the Thouless time, shifts to shorter times as contributions from longer-range spectral distance are included.
  arXiv  Detail & Related papers  (2023-11-15T19:00:01Z)
• Thermal equilibrium in Gaussian dynamical semigroups [77.34726150561087]
  We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices.
  arXiv  Detail & Related papers  (2022-07-11T19:32:17Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.