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
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