DOI: 10.5061/dryad.44j0zpct9
title: Data from: Phase transition of topological index driven by dephasing

description: 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.
description: # Data from: Phase transition of topological index driven by dephasing
 Dataset DOI: [10.5061/dryad.44j0zpct9](10.5061/dryad.44j0zpct9) ##
 Description of the data and file structure ### Files and variables ####
 File: fig1c_data.csv **Description:** Data for Fig. 1c of the manuscript.
 Lists values of (\gamma, g_c) denoting the analytic phase boundary (in
 red) of the dephased Chern insulator, where \gamma is the model tuning
 parameter (Eq. 3), and g_c is the critical dephasing strength for that
 value of \gamma. ##### Variables * \gamma versus g_c #### File:
 fig1a_data.csv **Description:** Data for Fig. 1a of the manuscript. Lists
 all eigenvalues of the flattened Hamiltonian H_C at \gamma=1.5 for each
 value of dephasing, g. ##### Variables * g versus eigenvalue number ####
 File: fig1b_data.csv **Description:** Data for Fig. 1b of the manuscript.
 Lists all eigenvalues of the flattened Hamiltonian H_C at \gamma=2.5 for
 each value of dephasing, g. ##### Variables * g versus eigenvalue number
 #### File: fig1e_data.csv **Description:** Data for Fig. 1e of the
 manuscript. Lists values of d\Delta_{sub}/dg, the derivative of the
 sub-matrix spectral gap with respect to dephasing strength, g, for the
 various system sizes at each value of g. ##### Variables *
 d\Delta_{\sub}/dg versus g #### File: fig3a_data.csv **Description:** Data
 for Fig. 3a of the manuscript. Lists disorder-averaged values of the Chern
 number, C, for each value of disorder strength, \delta, at various system
 sizes. ##### Variables * C versus \delta #### File: fig2_data.csv
 **Description:** Data for Fig. 2 of the manuscript. Lists values of
 (\delta t, g_c) denoting the analytic phase boundary (in red) of the 3D
 topological insulator, where \delta t is the model tuning parameter (Eq.
 5), and g_c is the critical dephasing strength. ##### Variables * g_c
 versus \delta t #### File: fig1d_data.csv **Description:** Data for Fig.
 1d of the manuscript. Lists values of the sub-matrix spectral gap,
 \Delta_{sub}, for the various system sizes at each value of dephasing
 strength, g. ##### Variables * \Delta_{sub} versus g #### File:
 fig3c_data.csv **Description:** This table contains the raw Chern number
 values (C) used to build the histogram in Fig. 3c. Each row shows one
 realization of the calculation, and the two columns correspond to
 different lattice sizes: a 6×6 system (left) and an 8×8 system (right).
 The numbers reflect how the computed Chern number fluctuates across
 realizations for each system size, with some values close to 0 and others
 near 2, showing the spread that the histogram summarizes. #### File:
 fig3b_data.csv **Description:** This table lists the individual Chern
 number values used to construct Fig. 3b. Each row corresponds to one
 numerical realization, and the two columns show results for two lattice
 sizes: 6×6 (left) and 8×8 (right). The values illustrate how the computed
 Chern number varies between realizations and between system sizes, forming
 the distribution shown in the figure.