Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, PR China.
Phys Rev Lett. 2013 May 24;110(21):210602. doi: 10.1103/PhysRevLett.110.210602. Epub 2013 May 21.
We study the behavior of the Rényi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Rényi entropies of different index α display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.
我们通过二维密度矩阵重整化群和解析方法研究了各向异性朗道模型在不同扰动下的重整化群流。我们发现，不同指标α的 Renyi 熵的导数具有相反的符号，这与典型的对称破缺态相反，并且无论相关长度如何，都可以在非常小的子系统上检测到。这种现象是由于在相位中存在一个具有平坦纠缠谱、零相关长度和纠缠熵的面积定律的点。我们认为，这种分裂在所有具有特定群论结构的相，包括量子双模型、团簇态和其他量子自旋液体中都是常见的。子系统的大小不需要与相关长度成比例的事实使得这种效应在实验上是可行的。
