莫特绝缘体、对偶和威尔逊圈中的非局部序
Non-local order in Mott insulators, Duality and Wilson Loops
摘要：
结果表明，在光晶格中玻色子的Mott绝缘相和超流相可以用一个非局域的“宇称序参量”来区分，这个“宇称序参量”可以通过单点分辨率成像直接获得.在一维中，格子玻色模型是一个经典的界面粗糙化问题的对偶。我们使用来自后者的已知精确结果来证明奇偶序参量在Mott绝缘相中表现出长程序，这与Endres等人最近的实验一致[Science 334，200（2011）]。在二维空间中，宇称序参量可以用2+1维非平凡U（1）规范理论的等时威尔逊圈来表示，它表现出库仑相和限制相之间的跃迁.宇称序参量的负对数在莫特绝缘体中服从周长律，在超流中被对数因子增强。
英文摘要：
It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [Science 334, 200 (2011)]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1) gauge theory in 2+1 dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.
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