AI 中文总结
本研究提出一种基于算符流形的变分框架，利用平稳作用量原理近似量子时间演化算符，可导出非微扰有效Floquet哈密顿量，在多种受驱量子系统中精度优于低阶Magnus展开，适用于一般含时量子系统。
AI 中文摘要
我们提出了一种在具有物理动机的算符流形内近似时间演化算符$\boldsymbol{\bar{U}(t)}$的变分框架，利用平稳作用量原理将量子动力学重新表述为算符空间中可处理的问题。对于周期驱动系统，得到的近似演化算符可直接导出有效Floquet哈密顿量，为传统的基于展开的方法提供了一种非微扰替代方案。该框架可通过扩大算符库实现系统性改进，并能自然纳入对称性与物理约束。当算符流形选自截断Magnus展开的项时，变分过程可在受限空间内有效重求和Magnus级数，显著提升精度。我们在受驱Rabi模型、受驱Lipkin-Meshkov-Glick模型和一维受驱Ising链上对该方法进行了基准测试，得到的有效Floquet哈密顿量系统性地比低阶Magnus展开更准确，尤其是在后者收敛性较差的区域，并展示了其对具有指数大希尔伯特空间的系统的适用性。尽管我们在此聚焦于Floquet系统，该形式体系同样适用于一般含时哈密顿量，为非平衡量子动力学提供了一种通用工具。
英文摘要
We introduce a variational framework for approximating the time-evolution operator $\hat{U}(t)$ within a physically motivated operator manifold, reformulating quantum dynamics as a tractable problem in operator space using stationary action principle. For periodically driven systems, the resulting approximate evolution operator directly yields an effective Floquet Hamiltonian, offering a non-perturbative alternative to conventional expansion-based methods. The framework is systematically improvable by enlarging the operator pool and naturally incorporates symmetries and physical constraints. When the operator manifold is chosen from the terms of a truncated Magnus expansion, the variational procedure effectively resums the Magnus series within the restricted space, significantly enhancing accuracy. We benchmark the approach on the driven Rabi model, the driven Lipkin-Meshkov-Glick model, and the one-dimensional driven Ising chain, yielding effective Floquet Hamiltonians that are systematically more accurate than low-order Magnus expansions, particularly in regimes where the latter converge poorly, and illustrating applicability to systems with exponentially large Hilbert spaces. Although we focus here on Floquet systems, the formalism applies equally to generic time-dependent Hamiltonians, providing a versatile tool for non-equilibrium quantum dynamics.
