Frérot Irénée, Roscilde Tommaso
Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France.
Phys Rev Lett. 2016 May 13;116(19):190401. doi: 10.1103/PhysRevLett.116.190401. Epub 2016 May 11.
We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation-the slave-boson approach-allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid-Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement-verified in all the phases-exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum-while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.
我们研究了典型的玻色 - 哈伯德模型的纠缠熵和纠缠谱，该模型描述了晶格上强相互作用的玻色子。通过使用一种可控的近似方法——从玻色子方法，我们能够以最小的代价研究该模型所有区域（最重要的是跨越其超流 - 莫特绝缘体转变）的纠缠情况。我们发现，在所有相中都得到验证的纠缠面积律标度在转变处呈现出尖锐的奇异性。当在固定的整数填充下跨越转变时，由于更丰富的纠缠谱包含一个额外的无隙模式，该奇异性会大大增强，这个无隙模式源自全局激发谱的振幅（希格斯）模式，而在具有可变填充的一般（ commensurate - incommensurate）转变中，该模式仍然是有隙的。因此，纠缠性质包含了玻色 - 哈伯德模型所展现的两种不同形式的玻色子临界性的独特特征。
