Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

Published
Source
arXiv
Paper number
832
Field
Research
arXiv ID
2608.04850

Key points

  • The paper proves that the diagonal and subdiagonal coefficients in the Arnoldi reduction of a non-Hermitian Hamiltonian exactly match the Flaschka variables of the two-dimensional Toda lattice.
  • This Toda structure closes without determining the remaining upper Hessenberg terms of the Arnoldi matrix.
  • The square of the subdiagonal coefficient determines the Fubini-Study metric and Berry curvature of the Krylov subspace.
  • Along the actual path, the Arnoldi frame generates exact isospectral transport and realizes counterdiabatic driving.
  • The paper confirms that the Hermitian limit reduces to the classical Toda-Lanczos correspondence.

Paper links

External research summaries. These are not HDATF publications or measured product results.

Read original (opens in a new tab)