Real-space many-body marker for correlated Z2 topological insulators

Taking the clue from the modern theory of polarization [Rev. Mod. Phys. 66, 899 (1994)], we identify an operator to distinguish between Z2-even (trivial) and Z2-odd (topological) insulators in two spatial dimen-sions. Its definition extends the position operator [Phys. Rev. Lett. 82, 370 (1999)], which was introduced in one-dimensional systems. We first show a few examples of noninteracting 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.

Automated summary

Drawing on the modern theory of polarization, this study proposes an operator to distinguish between different types of insulators in two-dimensional space. The operator, an extension of the position operator, is validated on various system sizes and applied to interacting models. Computation in the Fock space allows for direct calculation of ground-state wave functions, enabling investigation of strongly correlated topological insulators and other interacting systems.