从福克空间碎裂得到精确刚度与动力学响应
Exact Stiffness and Dynamical Responses from Fock-Space Fragmentation
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中文总结 AI 辅助
该研究利用福克空间碎裂的强可解性，证明量子几何嵌套模型的刚度精确等于高斯流形的变分取值，可精确获取多种动力学响应相关物理量，验证了量子多体自举的一项猜想。
中文摘要 AI 辅助
精确可解的量子多体模型十分稀少，即便其能谱具有代数结构，动力学响应通常仍难以获取，因为这类响应涉及大量激发态。本文表明，量子几何嵌套（QGN）模型具有一种源于福克空间碎裂（Fock-space fragmentation）的极强可解性：精确无挫折基态之上的激发会解耦为具有固定粒子与空穴算符数的克雷洛夫子空间，因此保持动力学不变性。利用该结构，我们证明QGN模型中自发破缺连续对称性的刚度精确等于其在高斯流形中的变分取值，验证了量子多体自举（quantum many-body bootstrap）的一项猜想[GaoHanKhalaf2026]。该证明显示，无穷小相位扭曲仅将基态耦合到单粒子-单空穴碎片，这与变分流形内基态的切空间重合，从而使变分曲率精确成立。更一般地，作用保持在固定福克空间碎片内的微扰，其响应函数由相应少体区精确决定，可精确获取静态磁化率、光电导率、动力学结构因子及单粒子格林函数等物理量。
英文摘要
Exactly solvable quantum many-body models are rare, and even when their spectra are algebraically organized, dynamical responses generally remain difficult to obtain because they probe an extensive number of excited states. Here we show that quantum geometric nesting (QGN) models admit an unusually strong form of solvability rooted in \emph{Fock-space fragmentation}: excitations on top of the exact frustration-free ground states decouple into Krylov subspaces with a fixed number of particle and hole operators, and hence remain dynamically invariant. Exploiting this structure, we prove that the stiffness of the spontaneously broken continuous symmetry in QGN models is exactly equal to its variational value in the Gaussian manifold, confirming a conjecture from quantum many-body bootstrap~\cite{GaoHanKhalaf2026}. The proof shows that an infinitesimal phase twist couples the ground state only to the one-particle, one-hole fragment, which coincides with the tangent space of the ground state within the variational manifold, thereby making the variational curvature exact. More generally, perturbations whose action remains within a fixed Fock-space fragment have response functions determined exactly by the corresponding few-body sector, enabling exact access to quantities including static susceptibility, optical conductivity, dynamical structure factors, and single-particle Green's functions.
