多体量子自旋系统的极值态
Extremal States of Multipartite Quantum Spin Systems
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中文总结 AI 辅助
本文研究多部量子自旋系统的极值态，识别反铁磁海森堡模型的三个相及阻挫判据，核心方法基于量子德菲内蒂定理。
中文摘要 AI 辅助
我们考虑在$k$部图上的两个量子自旋模型。假设系统在任意$k$个集合内的所有置换下保持不变。在无穷多粒子的极限下，由于量子德菲内蒂定理的一个版本，吉布斯态被描述为独立自旋的混合。首先，我们研究一个自旋-1/2反铁磁海森堡模型并识别其三个相。在低温下，所有$k$个集合都被磁化但相互抵消；在中等温度下，存在净磁场；在高温下，没有磁化。磁化温度是$k$次多项式的解。其次，我们允许一般自旋$s$，并识别所有具有阻挫的正交不变模型。无阻挫模型的标准是$k$个集合可以被分成两部分，其中唯一的反铁磁相互作用发生在两部分之间。
英文摘要
We consider two quantum spin models on $k$-partite graphs. The system is assumed to be invariant under all permutations within any of the $k$ sets. In the limit of infinitely many particles, the Gibbs state is described as a mixture of independent spins due to a version of the Quantum de Finetti theorem. First, we study a spin-1/2 antiferromagnetic Heisenberg model and identify its three phases. At low temperature all $k$ sets are magnetised but cancel each other, at medium temperature there is a net magnetic field and at high temperature there is no magnetisation. The magnetisation temperature is a solution to a $k$-degree polynomial. Second, we allow a general spin $s$ and identify all orthogonally invariant models which have frustration. The criterium for a frustration-free model is that the $k$-sets can be partitioned into two parts, where the only antiferromagnetic interaction is between the two parts.
