Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.
Phys Rev Lett. 2011 Dec 23;107(26):260602. doi: 10.1103/PhysRevLett.107.260602. Epub 2011 Dec 22.
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
我们提出了一种研究量子系统中受挫的一般方案。我们为任意量子系统引入了一种通用的受挫度量，并通过一个精确的不等式将其与一类纠缠单调相关联。如果给定哈密顿量的所有（纯）基态都满足这个不等式，那么这个系统就被称为不等式饱和。我们引入了量子自旋系统满足不等式饱和的充分条件，并通过广泛的数值测试验证了它们。这些条件为经典无受挫系统的图卢兹判据提供了量子领域的推广。满足这些条件的模型可以被合理地识别为几何上无受挫且仅受到纯量子起源的受挫的影响。因此，我们的结果为研究受挫的几何和量子贡献的交织提供了一个统一的框架。
