论文标题
海森伯格模特和舒尔 - weyl二元性
Heisenberg models and Schur--Weyl duality
论文作者
论文摘要
我们对具有不均匀（非随机）平均场相互作用的某些量子自旋系统进行了详细分析。示例包括但不限于完整的两部分图上的互换和旋转单线投影相互作用。使用Schur的表示理论框架的两个实例 - Weyl二元性，我们可以在我们考虑的模型中明确计算自由能和其他热力学限制。这使我们能够描述相变，地面相图和极端状态的预期结构。
We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.
