论文标题
相关的真实空间多体标记$ {\ Mathbb Z} _2 $拓扑绝缘子
A real-space many-body marker for correlated ${\mathbb Z}_2$ topological insulators
论文作者
论文摘要
从现代极化理论中汲取线索[R. Resta，修订版Mod。物理。 {\ bf 66}，899（1994）]，我们确定一个操作员，以区分$ {\ mathbb z} _2 $ - eve（Trivial）和$ {\ Mathbb Z} _2 _2 _2 $ -ODD（TOPOLICAGION）在两个空间尺寸中的绝缘子。它的定义扩展了位置操作员[R. Resta和S. Sorella，物理。莱特牧师。 {\ bf 82}，370（1999）]，它是在一维系统中引入的。我们首先显示了一些非相互作用模型的示例，其中定义了单粒子波函数，并可以直接与大型系统大小的标准技术进行直接比较。然后，我们说明了其适用于在一个小群集上的相互作用模型的适用性，那里有精确的对角线化。它在Fock空间中的公式可以直接计算地面波函数（或IT的任何近似值）上的期望值，从而使我们能够研究一般的交互系统，例如强相关的拓扑绝缘子。
Taking the clue from the modern theory of polarization [R. Resta, Rev. Mod. Phys. {\bf 66}, 899 (1994)], we identify an operator to distinguish between ${\mathbb Z}_2$-even (trivial) and ${\mathbb Z}_2$-odd (topological) insulators in two spatial dimensions. Its definition extends the position operator [R. Resta and S. Sorella, Phys. Rev. Lett. {\bf 82}, 370 (1999)], which was introduced in one-dimensional systems. We first show a few examples of non-interacting models, where single-particle wave functions are defined and allow for a direct comparison with standard techniques on large system sizes. Then, we illustrate its applicability for an interacting model on a small cluster, where exact diagonalizations are available. Its formulation in the Fock space allows a direct computation of expectation values over the ground-state wave function (or any approximation of it), thus allowing us to investigate generic interacting systems, such as strongly-correlated topological insulators.
