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-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.
Related
- Spectral Theory of an Exactly Solvable Quantum-Optical Oscillator
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BibTeX
@misc{zhou2026diffusivity,
title = {{Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain}},
author = {Zhi-Li Zhou and Jorge Noronha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16559},
eprint = {2609.16559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16559},
}
RIS
TY - UNPB
TI - Diffusivity in Dissipative Quantum Transport from an Exactly Solvable Krylov Chain
AU - Zhi-Li Zhou
AU - Jorge Noronha
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16559
UR - https://arxiv.org/abs/2609.16559
AB - 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-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.
ER -