Quantum Spin Systems at Positive Temperature
Quantum Spin Systems at Positive Temperature
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正温度下的量子自旋系统
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Starr
中科院分区：
文献类型：
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作者：
M. Biskup;L. Chayes;S. Starr
我们开发了一种新的方法，在量子自旋模型的基础上，他们的经典对应物的相变。通过解释，我们证明了只要棋盘估计可以用来证明经典模型中的相变，相应的量子模型也会有类似的相变，只要逆温度β和量子自旋的大小满足计算器$$。从量子系统出发，我们要求它是反射正的，并且它有一个有意义的经典极限;核心技术估计可以描述为Berezin-Lieb不等式向下扩展到矩阵元素的水平。本文应用一般理论证明了具有$$mathcal{S} gg 1 $$的各种量子自旋系统中的相变。最著名的例子是$$mathbb{Z}^2$$上的量子轨道罗盘模型和$$mathbb{Z}^3$$上的量子120度模型，尽管它们的（经典）基态具有无限简并性，但它们在低温下表现出对称性破缺。
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$mathcal{S}$$ satisfy $$etallsqrtmathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$mathcal{S}gg1$$. The most notable examples are the quantum orbital-compass model on $$mathbb{Z}^2$$ and the quantum 120-degree model on $$mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.