论文标题
刚性转子中的浆果阶段：奇数抗fiferromagnets的新兴物理
Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets
论文作者
论文摘要
刚性转子是量子力学中的一个经典问题，描述了固定质量中心的刚体的动力学。此问题的配置空间为$ SO（3）$，这是所有旋转的三个维度的空间。这是一个拓扑空间，具有两种类型的闭环：可以绝热地缩小到一个无法达到点的琐碎回路，而非平凡的回路则不能。在该问题的传统表述中，固定状态在两种类型的闭环中都是周期性的。但是，如果引入浆果阶段，周期性条件可能会改变。我们认为，时间反向对称性仅允许一种新的可能性 - 所有非平凡环的$π$的浆果相。我们通过利用$（3）$和$ su（2）$空间之间的连接来得出相应的固定状态。在任何非平凡的环路上，即固定状态在任何轴上旋转$2π$旋转下，固定液在任何非平凡的环上都是抗周期性的。值得注意的是，该框架是在某些量子磁体的低能物理学中实现的。磁铁必须满足以下条件：（a）经典的基础状态不铝化，没有净磁化，（b）经典基础状态的集合由$ so（3）$索引，以及（c）（c）产品$ n \ times s $是半含量，$ n $是$ n $ n $是spins and $ s $是旋转量子量子量子。我们证明了这一结果是在具有奇数顶点的多边形上定义的海森堡抗fiferromagnets家族。在每个顶点，我们都有一个旋转的$ s $矩与最近的邻居耦合。在经典的极限中，这些磁铁具有共面基态。它们的量子光谱在低能时对应于“球形顶部”和“对称顶部”刚性转子。对于$ s $的整数值，我们恢复了传统的刚性转子光谱。有了Half-Integer-$ s $，我们获得了$π$的浆果阶段的转子光谱。
The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration space of this problem is $SO(3)$, the space of all rotations in three dimensions. This is a topological space with two types of closed loops: trivial loops that can be adiabatically shrunk to a point and non-trivial loops that cannot. In the traditional formulation of the problem, stationary states are periodic over both types of closed loops. However, periodicity conditions may change if Berry phases are introduced. We argue that time-reversal-symmetry allows for only one new possibility -- a Berry phase of $π$ attached to all non-trivial loops. We derive the corresponding stationary states by exploiting the connection between $SO(3)$ and $SU(2)$ spaces. The solutions are anti-periodic over any non-trivial loop, i.e., stationary states reverse sign under a $2π$ rotation about any axis. Remarkably, this framework is realized in the low-energy physics of certain quantum magnets. The magnets must satisfy the following conditions: (a) the classical ground states are unpolarized, carrying no net magnetization, (b) the set of classical ground states is indexed by $SO(3)$, and (c) the product $N\times S$ is a half-integer, where $N$ is the number of spins and $S$ is the spin quantum number. We demonstrate this result in a family of Heisenberg antiferromagnets defined on polygons with an odd number of vertices. At each vertex, we have a spin-$S$ moment that is coupled to its nearest neighbours. In the classical limit, these magnets have coplanar ground states. Their quantum spectra, at low energies, correspond to `spherical top' and `symmetric top' rigid rotors. For integer values of $S$, we recover traditional rigid rotor spectra. With half-integer-$S$, we obtain rotor spectra with a Berry phase of $π$.
