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

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.

Published version

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Cited by in corpus (9)

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• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension
• Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz
• Real-space topology and charge order in the Haldane-Holstein Model