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arXiv 0706.4258cond-mat.str-elcond-mat.stat-mech
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二维费米子绝缘态的表征

Characterization of two-dimensional fermionic insulating states

Ryuichi Shindou, Ken-Ichiro Imura, Masao Ogata

摘要:

受二维空间中超导体与绝缘体之间的对偶关系的启发,我们推测适合于描述二维费米子绝缘态的序参量是通常在统计变换中已知的无序算符.也就是说,无序算子的相位沿着闭环的变化测量容纳在该环内的粒子密度。因此,将这种(掺杂的)粒子密度与2D SC中的磁感应强度的对偶对应物识别,我们可以自然地引入无序算子作为2D绝缘体的对偶序参量。无序算子有一个从这个"漩涡“到单个无限远点的分支切割。为了检验这一猜想对任意的二维晶格模型,我们选择了这个分支切割是兼容的周期性边界条件,并获得了一般形式的期望值的非相互作用的金属/绝缘体波函数,包括带隙的平均场阶波函数。基于这个表达式,我们分析观察到,它确实消失了一个广泛的类带金属的热力学极限。另一方面,在绝缘状态下,它被局域化长度或被称为量子度规张量的实值规范不变量2-量化。

英文摘要:

Inspired by the duality picture between superconductivity and insulator in two spatial dimension, we conjecture that the order parameter, suitable for characterizing 2D fermionic insulating state, is the disorder operator, usually known in the context of statistical transformation. Namely, the change of the phase of the disorder operator along a closed loop measures the particle density accommodating inside this loop. Thus, identifying this (doped) particle density with the dual counterpart of the magnetic induction in 2D SC, we can naturally introduce the disorder operator as the dual order parameter of 2D insulators. The disorder operator has a branch cut emitting from this ``vortex'' to the single infinitely far point. To test this conjecture against an arbitrary 2D lattice models, we have chosen this branch cut to be compatible with the periodic boundary condition and obtain a general form of its expectation value for non-interacting metal/insulator wavefunction, including gapped mean-field order wavefunction. Based on this expression, we observed analytically that it indeed vanishes for a wide class of band metals in the thermodynamic limit. In insulating states, on the other hand, it is quantified by the localization length or the real-valued gauge invariant 2-from dubbed as the quantum metric tensor.

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