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This research presents an exact analytical solution for transport coefficients in a dissipative quantum spin chain using a novel Krylov-space mechanism, overcoming the typical inaccessibility of such calculations in interacting many-body systems. By mapping the dynamics to a self-similar semi-infinite chain with a boundary defect, the study derives precise corrections to Green-Kubo diffusivity and determines all relevant Lanczos coefficients exactly. These findings advance theoretical understanding of quantum transport regimes where dissipation dominates, offering new mathematical tools for analyzing open quantum systems.
Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain
arXiv:2609.16559v1 Announce Type: cross 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.
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)
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