有序量子相的经典性质与自发对称性破缺的起源
Classical nature of ordered quantum phases and origin of spontaneous symmetry breaking
摘要：
我们通过研究长期存在的猜想，即最大对称性破缺的量子基态是对应于全局有序相的最经典的量子态，分析了复杂量子系统中自发对称性破缺的本质。我们通过比较不同的局部和全局指标的经典性和量子性，分别在破缺和保缺的量子基态，这一论点定量精确。我们首先讨论如何天真地比较本地，成对纠缠和不和谐显然会导致相反的结论。事实上，我们表明，在保量子基态的两体纠缠捕获的总两体量子关联的一小部分，而相反，在最大的破缺基态，它的贡献最大的量的总两体量子关联。然后，我们通过观察量子基态的整体宏观相关性质来检验这个猜想。我们证明了与全局有序相相关联的实现哈密顿对称性最大破缺的基态是唯一的：I）总是局部可转换的，即可以从所有其他基态通过仅应用LOCC变换获得（本地操作和经典通信），而反过来是永远不可能的; II）最小化一夫一妻制在全局共享的宏观二部纠缠上的不平等。
英文摘要：
We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a globally ordered phase. We make this argument quantitatively precise by comparing different local and global indicators of classicality and quantumness, respectively in symmetry-breaking and symmetry-preserving quantum ground states. We first discuss how naively comparing local, pairwise entanglement and discord apparently leads to the opposite conclusion. Indeed, we show that in symmetry-preserving ground states the two-body entanglement captures only a modest portion of the total two-body quantum correlations, while, on the contrary, in maximally symmetry-breaking ground states it contributes the largest amount to the total two-body quantum correlations. We then put to test the conjecture by looking at the global, macroscopic correlation properties of quantum ground states. We prove that the ground states which realize the maximum breaking of the Hamiltonian symmetries, associated to a globally ordered phase, are the only ones that: I) are always locally convertible, i.e. can be obtained from all other ground states by only applying LOCC transformations (local operations and classical communication), while the reverse is never possible; II) minimize the monogamy inequality on the globally shared, macroscopic bipartite entanglement.
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