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arXiv · 1308.4900

Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus

Zhong Wang·Shou-Cheng Zhang
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Abstract

We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $θ$ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interaction and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula, and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

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Zhong Wang, Shou-Cheng Zhang. 2014-01-25. Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus. https://doi.org/10.1103/physrevx.4.011006

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