Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain

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.

Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)

arXiv:2609.16559 [cond-mat.stat-mech]

(or arXiv:2609.16559v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.16559 arXiv-issued DOI via DataCite (pending registration)