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

Zhong Wang: Shou-Cheng Zhang; Physical Review X, 01/21/14.

Additional Authors: Shou-Cheng Zhang

Abstract:

We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions 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.