Bayat Abolfazl, Johannesson Henrik, Bose Sougato, Sodano Pasquale
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden.
Nat Commun. 2014 May 7;5:3784. doi: 10.1038/ncomms4784.
A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. The resulting quantum fluctuations which trigger the transition produce scaling behaviour of various observables, governed by universal critical exponents. A particularly interesting class of such transitions appear in systems with quantum impurities where a non-extensive term in the free energy becomes singular at the critical point. Curiously, the notion of a conventional order parameter that exhibits scaling at the critical point is generically missing in these systems. Here we explore the possibility to use the Schmidt gap, which is an observable obtained from the entanglement spectrum, as an order parameter. A case study of the two-impurity Kondo model confirms that the Schmidt gap faithfully captures the scaling behaviour by correctly predicting the critical exponent of the dynamically generated length scale at the critical point.
当控制场或相互作用发生变化时，量子相变可能会在零温度下系统的基态中出现。引发相变的量子涨落会产生各种可观测量的标度行为，这些行为由普适临界指数支配。在具有量子杂质的系统中会出现一类特别有趣的此类相变，其中自由能中的非广延项在临界点处变得奇异。奇怪的是，这些系统中通常缺少在临界点表现出标度行为的传统序参量的概念。在此，我们探讨将施密特间隙用作序参量的可能性，施密特间隙是从纠缠谱中获得的一个可观测量。对双杂质近藤模型的案例研究证实，施密特间隙通过正确预测临界点处动态生成长度尺度的临界指数，忠实地捕捉了标度行为。
