Quantum superintegrable spin systems on graph connections

Nicolai Reshetikhin, Jasper Stokman
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Abstract

In this paper we construct certain quantum spin systems on moduli spaces of -connections on a connected oriented finite graph, with a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum Hamiltonians in terms of local invariant tensors. We determine sufficient conditions ensuring superintegrability of the quantum spin system using irreducibility criteria for Harish-Chandra modules due to Harish-Chandra and Lepowsky & McCollum. The resulting class of quantum superintegrable spin systems includes the quantum periodic and open spin Calogero–Moser spin chains as special cases. In the periodic case the description of the joint eigenfunctions in terms of local invariant tensors are multipoint generalized trace functions, in the open case multipoint spherical functions on compact symmetric spaces.
图连接上的量子超可积自旋系统
在本文中,我们构建了某些量子自旋系统,这些量子自旋系统位于连通的定向有限图上的-连接的模空间上,并带有一个简单连通的紧凑李群。我们用局部不变张量构建了共价量子哈密顿的联合特征函数。我们利用哈里什-钱德拉(Harish-Chandra)和勒波斯基与麦科勒姆(Lepowsky & McCollum)提出的哈里什-钱德拉模块的不可还原性标准,确定了确保量子自旋系统超稳定性的充分条件。由此产生的量子超可整合自旋系统类别包括量子周期和开放自旋卡洛吉罗-莫泽自旋链等特例。在周期情况下,用局部不变张量描述的联合特征函数是多点广义迹函数;在开放情况下,是紧凑对称空间上的多点球形函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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