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arXiv 2202.12207cond-mat.str-el
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相关${\mathbb Z}_2$拓扑绝缘体的实空间多体标记

A real-space many-body marker for correlated ${\mathbb Z}_2$ topological insulators

Ivan Gilardoni, Federico Becca, Antimo Marrazzo, Alberto Parola

摘要:

以现代极化理论为线索[R. Resta,Rev. Mod. Phys. { \bf 66},899(1994)]中,我们确定了一个算子来区分两个空间维度中的${\mathbb Z}_2$ -偶(平凡)和${\mathbb Z}_2$ -奇(拓扑)绝缘体。它的定义推广了位置算子[R. Resta和S. Sorella,Phys. Rev. Lett. { \bf 82},370(1999)],其在一维系统中引入。我们首先展示了几个例子,非相互作用的模型,单粒子波函数的定义,并允许与标准技术的大系统尺寸的直接比较。然后,我们说明了它的适用性的相互作用模型上的一个小集群,精确的对角化。它在Fock空间中的公式允许直接计算基态波函数(或其任何近似)的期望值,从而使我们能够研究一般的相互作用系统,如强相关的拓扑绝缘体。

英文摘要:

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.

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