Mondragon-Shem Ian, Khan Mayukh, Hughes Taylor L
Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.
Phys Rev Lett. 2013 Jan 25;110(4):046806. doi: 10.1103/PhysRevLett.110.046806.
The use of quantum entanglement to study condensed matter systems has been flourishing in critical systems and topological phases. Additionally, using real-space entanglement one can characterize localized and delocalized phases of disordered fermion systems. Here we instead propose the momentum-space entanglement spectrum as a means of characterizing disordered models. We show that localization in one dimension can be characterized by the momentum space entanglement between left and right movers and illustrate our methods using explicit models with spatially correlated disorder that exhibit phases which avoid complete Anderson localization. The momentum space entanglement spectrum clearly reveals the location of delocalized states in the energy spectrum, can be used as a signature of the phase transition between a delocalized and localized phase, and only requires a single numerical diagonalization to yield clear results.
利用量子纠缠研究凝聚态系统在临界系统和拓扑相中蓬勃发展。此外，通过实空间纠缠可以表征无序费米子系统的局域相和非局域相。在此，我们提出将动量空间纠缠谱作为表征无序模型的一种手段。我们表明，一维中的局域化可以通过左右移动者之间的动量空间纠缠来表征，并使用具有空间相关无序的显式模型来说明我们的方法，这些模型展现出避免完全安德森局域化的相。动量空间纠缠谱清楚地揭示了能谱中离域态的位置，可作为离域相和局域相之间相变的标志，并且只需要一次数值对角化就能得出清晰的结果。
