二维费米子绝缘态的表征

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摘要翻译：
受超导与绝缘体在二维空间上的对偶图的启发，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，无序算符的相位沿闭环的变化度量了该闭环内所容纳的粒子密度。因此，用二维SC中的磁感应强度的对偶来识别这种（掺杂）粒子密度，我们就可以自然而然地引入无序算符作为二维绝缘体的对偶序参量。无序算符有一个分支切割，从这个“旋涡”发射到单个无限远的点。为了在任意二维晶格模型上验证这一猜想，我们选择了与周期边界条件相容的分支割，并得到了它对非相互作用金属/绝缘体波函数（包括间隙平均场阶波函数）期望值的一般形式。基于这个表达式，我们解析地观察到，在热力学极限下，对于一大类能带金属，它确实消失了。另一方面，在绝缘态中，它由局域长度或实值规范不变量2-from量化，称为量子度量张量。
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英文标题：
《Characterization of two-dimensional fermionic insulating states》
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作者：
Ryuichi Shindou, Ken-Ichiro Imura, Masao Ogata
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Strongly Correlated Electrons        强关联电子
分类描述：Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学，非费米液体，自旋液体，量子临界性，电荷密度波，金属-绝缘体跃迁
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

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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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PDF链接：
https://arxiv.org/pdf/706.4258

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关键词：localization Statistical Transitions Dimensional equilibrium 分支 规范 解析 parameter 二维