耦合自旋电子动力学中的突现非阿贝尔规范理论
Emergent Non-Abelian Gauge Theory in Coupled Spin-Electron Dynamics
摘要：
控制“慢”和“快”自由度动力学的时间尺度的明确分离通常是独立低能理论出现的先决条件。在这里，我们考虑（慢）经典自旋交换耦合到（快）传导电子的紧束缚系统。在电子系统的量子态在任意时刻$t$处于对应于$t$自旋组态的$n$维低能子空间的约束下，导出了有效的运动方程.有效低能理论直接展开，并采取非阿贝尔规范理论的形式，其规范自由度由跨越瞬时低能扇区的基的任意性给出。完整约束在经典自旋的运动方程中产生了一个规范协变的自旋-Berry曲率张量。在$n>1$的非阿贝尔理论中，与$n=1$绝热自旋动力学理论相反，自旋-贝里曲率一般是非零的，即使对于时间反演对称系统也是如此。它的期望值与电子态的表示是规范不变的，并产生一个额外的{ \em几何}自旋力矩。除了反常进动，$n\ge 2$理论还捕获了自旋章动，这通常被认为是一种延迟效应。这是证明了一个极小模型与一个单一的经典自旋的原理数值计算。已经为$n=2$和参数制度的$n=1$绝热理论崩溃，我们发现很好的协议从完整的（无约束）理论得到的结果。
英文摘要：
A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange coupled to a tight-binding system of (fast) conduction electrons. The effective equations of motion are derived under the constraint that the quantum state of the electron system at any instant of time $t$ lies in the $n$-dimensional low-energy subspace for the corresponding spin configuration at $t$. The effective low-energy theory unfolds itself straightforwardly and takes the form of a non-abelian gauge theory with the gauge freedom given by the arbitrariness of the basis spanning the instantaneous low-energy sector. The holonomic constraint generates a gauge covariant spin-Berry curvature tensor in the equations of motion for the classical spins. In the non-abelian theory for $n>1$, opposed to the $n=1$ adiabatic spin dynamics theory, the spin-Berry curvature is generically nonzero, even for time-reversal symmetric systems. Its expectation value with the representation of the electron state is gauge invariant and gives rise to an additional {\em geometrical} spin torque. Besides anomalous precession, the $n\ge 2$ theory also captures the spin nutational motion, which is usually considered as a retardation effect. This is demonstrated by proof-of-principle numerical calculations for a minimal model with a single classical spin. Already for $n=2$ and in parameter regimes where the $n=1$ adiabatic theory breaks down, we find good agreement with results obtained from the full (unconstrained) theory.
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