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arXiv · 2202.12207

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

Ivan Gilardoni·Federico Becca·Antimo Marrazzo·Alberto Parola
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Abstract

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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Ivan Gilardoni, Federico Becca, Antimo Marrazzo, Alberto Parola. 2022-02-24. A real-space many-body marker for correlated ${\mathbb Z}_2$ topological insulators. https://doi.org/10.1103/physrevb.106.l161106

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