Data from: Phase transition of topological index driven by dephasing

We study topological insulators under dephasing noise. With examples of
both a 2d Chern insulator and a 3d topological insulator protected by
time-reversal symmetry, we demonstrate that there is a phase transition at
finite dephasing strength between phases with nontrivial and trivial
topological indices. Here, the topological index is defined through the
correlation matrix. The transition can be diagnosed through the spectrum
of the whole correlation matrix or of a local subsystem. Interestingly,
even if the topological insulator is very close to the topological-trivial
critical point in its Hamiltonian, it still takes a finite strength of
dephasing to change the topological index, suggesting the robustness of
topological insulators under dephasing. In the case of Chern insulator,
this robustness of the phase with nontrivial Chern number persists near
the critical point between the topological and Anderson insulator, which
is tuned by the strength of disorder in the Hamiltonian.