论文标题
通过平均场schrödinger方程的经典自旋动力学的几何整合
Geometric integration of classical spin dynamics via a mean-field Schrödinger equation
论文作者
论文摘要
Landau-Lifshitz方程描述了磁偶极子的时间进化，可以通过取量子机械旋转的哈密顿量的经典极限来得出。为了达到这一限制，人们将多体量子状态限制在连贯状态的张量产品上，从而忽略了站点之间的纠缠。量子自旋算子的期望值产生通常的经典自旋偶极子。人们还可以考虑自旋算子多项式的预期值，从而导致四倍和高阶自旋矩，这满足了动态运动方程式，该运动方程将Landau-Lifshitz动力学概括[Zhang and Batista，phys。修订版B 104，104409（2021）]。在这里，我们将这些$ n^2-1 $概括的旋转组件的动态重新制定为在$ n $维相干状态上的平均场Schrödinger方程。该观点提出了尊重经典自旋动力学的局部符号结构的有效整合方法。
The Landau-Lifshitz equation describes the time-evolution of magnetic dipoles, and can be derived by taking the classical limit of a quantum mechanical spin Hamiltonian. To take this limit, one constrains the many-body quantum state to a tensor product of coherent states, thereby neglecting entanglement between sites. Expectation values of the quantum spin operators produce the usual classical spin dipoles. One may also consider expectation values of polynomials of the spin operators, leading to quadrupole and higher-order spin moments, which satisfy a dynamical equation of motion that generalizes the Landau-Lifshitz dynamics [Zhang and Batista, Phys. Rev. B 104, 104409 (2021)]. Here, we reformulate the dynamics of these $N^2-1$ generalized spin components as a mean-field Schrödinger equation on the $N$-dimensional coherent state. This viewpoint suggests efficient integration methods that respect the local symplectic structure of the classical spin dynamics.
