算符反射正性不等式及其在相互作用量子转子中的应用
Operator reflection positivity inequalities and their applications to interacting quantum rotors
摘要：
在反射正性理论及其对统计力学系统的应用中，某些矩阵不等式起着核心作用。Dyson-Lieb-Simon不等式和Dyson-Lieb-Shastry-Schupp不等式是突出的例子。本文将KLS-S不等式推广到矩阵被某些算子取代的情形。作为应用，我们证明了二维量子转子的基态中存在长程序。
英文摘要：
In the Reflection Positivity theory and its application to statistical mechanical systems, certain matrix inequalities play a central role. The Dyson-Lieb-Simon and Kennedy-Lieb-Shastry-Schupp inequalities constitute prominent examples. In this paper we extend the KLS-S inequality to the case where matrices are replaced by certain operators. As an application, we prove the occurrence of the long range order in the ground state of two-dimensional quantum rotors.
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