发表机构
Illinois Center for Advanced Studies of the Universe Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系伊利诺伊宇宙高级研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种新的Krylov空间机制，在强耗散一维XXZ链中精确计算Green-Kubo扩散率的领先密度依赖修正，并解析求解边界Green函数，揭示其沿Krylov链指数衰减。
AI 中文摘要
相互作用量子多体系统中输运系数的计算很少能解析地进行。在这里，我们发展了一种新的Krylov空间机制，使得在一维含噪声的自旋-1/2 XXZ链的强耗散区域中，对Green-Kubo扩散率的领先密度依赖修正可以精确计算。这是通过证明密度极化修饰的键相干性生成一个Krylov子空间来实现的，在该子空间中，耗散器的重复作用恰好闭合在一个明确可识别的算子族上。在这个子空间内，耗散动力学随后被映射到一个带有边界缺陷的自相似半无限链上。令人惊讶的是，Krylov链的所有Lanczos系数及其边界Green函数都可以精确确定。后者随后决定了扩散率的精确领先密度依赖修正。最后，我们解析地计算了完整的边界到体Green函数，并发现它沿着涌现的Krylov链呈指数衰减。
英文摘要
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.
Comments7 pages
