Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain

• URL: http://arxiv.org/abs/2609.16559v1
• Date: Tue, 15 Sep 2026 02:56:17 GMT
• Title: Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain
• Abstract summary: We make the leading density dependent correction to Green-Kubo diffusivity emphexactly calculable in a noisy spin-$frac12$ XXZ chain.<n>Surprisingly, emphall Lanczos coefficients of the Krylov chain and its boundary Green's function can be determined exactly.
• Score: 15.895680728942777
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The computation of transport coefficients in interacting quantum many-body systems is rarely analytically accessible. Here, we develop a new Krylov-space mechanism that makes the leading density dependent correction to Green-Kubo diffusivity \emph{exactly} calculable in the strong-dissipation regime of a one-dimensional noisy spin-$\frac{1}{2}$ XXZ chain. This is done by showing that the density-polarization-dressed bond coherence generates a Krylov subspace where repeated action of the dissipator closes exactly on an explicitly identifiable operator family. Within this subspace, the dissipative dynamics is then mapped onto a self-similar semi-infinite chain with a boundary defect. Surprisingly, \emph{all} Lanczos coefficients of the Krylov chain and its boundary Green's function can be determined exactly. The latter then determines the exact leading density-dependent correction to the diffusivity. Finally, we calculate analytically the full boundary-to-bulk Green's function and find that it decays exponentially along the emergent Krylov chain.

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