AI 中文总结
本研究提出含时酉耦合簇理论，将其应用于电子量子动力学，通过生成元制备初态后传播，在硬核玻色-哈伯德环上测试并探讨其局限与扩展方向。
AI 中文摘要
本研究提出一种适用于电子量子动力学的含时（TD）酉耦合簇（UCC）形式，涵盖单参考与多参考 regime 下的激发态及其叠加态传播。标准含时耦合簇技术具备尺寸广延性，但依赖非厄米双变分作用泛函，会破坏时间可逆性，得到的跃迁矩阵元与振幅估计量呈非对称性（尽管准确且可系统改进）。本文将时间演化算符视为由含时反厄米簇算子与一阶生成元驱动的指数映射，应用狄拉克-弗伦克尔作用原理，提取出由类似海森堡绘景对易子支配的运动方程。该方法与此前的非厄米形式相联系，其中可观测量由正则与扩展簇算子表达，由此得到的生成元簇算子在未受扰含时极限下会导出 UCC 本征值问题。尽管该问题可达到精确性，但生成元的时间依赖性仅在短传播时间内成立，因此本文用生成元制备初态，再通过形式含时 UCC 运动方程传播该态。该理论在与中性原子链相关的扩展硬核玻色-哈伯德环上进行测试，同时探讨了理论当前的局限性与可能的扩展方向。
英文摘要
This work presents a time-dependent (TD) unitary coupled-cluster (UCC) formulation for electronic quantum dynamics, including the propagation of excited states and their superpositions, in both single- and multi-reference regimes. Standard TD coupled-cluster techniques offer size-extensivity, but they rely on non-Hermitian bivariational action functionals that break time-reversibility, giving transition matrix elements and amplitude estimators that are asymmetric (though accurate and systematically improvable). Here we use the time-evolution operator as an exponential map driven by TD anti-Hermitian cluster operators and first-order generators. Applying the Dirac-Frenkel action principle, we extract equations of motion governed by Heisenberg-picture-like commutators. This approach connects to our previous non-Hermitian formulations, where observables are expressed in terms of regular and extended cluster operators. From that connection we obtain a generator cluster operator whose unperturbed TD limit leads to the UCC eigenvalue problem. Even though this problem can be exact, the time dependence of the generator holds only at short propagation times, so we use the generator to prepare the initial state and then propagate that state with the formal TD UCC equation of motion. The theory is tested on an extended hard-core Bose-Hubbard ring with connections to neutral atom chains, and we discuss the theory's present limitations and possible extensions.
Comments41 pages, 7 figures
