AI 中文总结
研究量子系统实时动力学模拟受限时的数据高效重建方法，基于分数微积分开发盲分数包络外推法（fSD），在临界XXZ链等系统上比有限极点方法更准确，能盲目确定指数\(\alpha\)，是短模拟时间下量子临界动力学的有效途径。
AI 中文摘要
量子系统实时动力学模拟常受纠缠增长限制于短时间。有限极点重建在频谱为有限激发集时能可靠外推数据，但在临界点，低能谱是幂律连续统，有限极点无法表示。本文为此开发分数微积分激励的包络外推法。其结构受分数形式的施温格 - 戴森（fSD）方程启发，拉普拉斯符号\(s^{\alpha}\)解析携带分支切割，剩余自能保持亚纯。在实际数据中，在拟合窗口内盲目选择指数\(\alpha\)，信号通过\(t^{\alpha}\)去趋势，残差用稳定有限极点模型拟合并恢复代数包络。在临界XXZ链上，这种盲分数包络方法（简称fSD）比有限极点方法更准确地外推短时间数据，能盲目确定指数\(\alpha\)并包含弱耦合下的封闭形式卢廷格值。在\(\Delta = 1\)饱和转变处找到\(z = 2\)稀释磁振子指数\(\alpha = 1/2\)，在有能隙的自由磁振子相也有优势。在非临界动态平均场谱上，fSD无法选择稳定分数包络，退化为标准极点结果，当只有短模拟时间时，它是量子临界动力学的高效准确途径。
英文摘要
Simulating real-time dynamics of quantum systems is often limited to short times by entanglement growth. Finite-pole reconstructions such as linear prediction and related machineries extrapolate such data reliably when the spectrum is a finite set of excitations, but at criticality the low-energy spectrum is a power-law continuum $A(ω)\sim|ω|^{α-1}$ -- a branch cut whose real-time tail $G(t)\sim t^{-α}$ finitely many poles cannot represent. Here we develop a fractional-calculus-motivated envelope extrapolation for such data. Its structure is motivated by a fractional form of Schwinger--Dyson (fSD) equation, in which the Laplace symbol $s^α$ carries the branch cut analytically while the residual self-energy remains meromorphic. On real data we employ the corresponding operational alternative -- the exponent $α$ is selected blindly inside the fit window, the signal is detrended by $t^α$, the residual is fitted by a stabilized finite-pole model, and the algebraic envelope is restored. On the critical XXZ chain this blind fractional-envelope method (fSD for short) extrapolates short-time data typically several-fold more accurately than finite-pole methods, with the exponent $α$ identified blindly from the fit window alone and bracketing the closed-form Luttinger value at weak coupling. The same blind search finds the $z=2$ dilute-magnon exponent $α=1/2$ at the $Δ=1$ saturation transition, and the advantage persists in the gapped free-magnon phase with its sharp band edges. On noncritical dynamical mean-field spectra, whose low-frequency response is regular, fSD by contrast fails to select any stable fractional envelope and reduces to the standard pole result rather than manufacturing a spurious power law, making it an efficient and accurate route to quantum critical dynamics when only short simulation times are accessible.
Comments14 pages, 9 figures
