具有平均场相互作用的量子晶格系统的KMS条件与变分原理的等价性
On the Equivalence of the KMS Condition and the Variational Principle for Quantum Lattice Systems with Mean-Field Interactions
摘要：
我们将荒木关于短程相互作用量子晶格系统平衡态的KMS条件和变分原理等价性的著名结果推广到一类可能包含平均场相互作用（代表长程相互作用的极端形式）的模型中。这个结果让人想起了范·海曼关于平均场模型的平衡态的工作。我们最近的成果使这种扩展成为可能，这些成果是关于晶格上平均场模型的自由能量密度最小化的状态，以及这些模型的无限体积动力学。
英文摘要：
We extend Araki's well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of models possibly containing mean-field interactions (representing an extreme form of long-range interactions). This result is reminiscent of van Hemmen's work on equilibrium states for mean-field models. The extension was made possible by our recent outcomes on states minimizing the free energy density of mean-field models on the lattice, as well as on the infinite volume dynamics for such models.
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