Fig. 3: Weak noise regime of the non-Hermitian QAH model.

a Spin polarization 〈σ(k, t)〉 under four different white noise configurations at momentum k = (1.286, −0.257). No notable decay is observed for a single type of noise. b Corresponding stochastic averaged spin polarization s(k, t) over all noise configurations and the rescaled spin polarization \(\tilde{{{{\bf{s}}}}}({{{\bf{k}}}},t)\), which has the minimum oscillation frequency ω on the dBIS at momentum k = (1.286, −0.257). The system is dissipative after stochastic average as an outcome of non-Hermitian dynamics. c Time-averaged rescaled spin polarizations \(\overline{{\tilde{s}}_{i}({{{\bf{k}}}})}\) for fixed k_y = −0.257 and k_x ∈ [−1.8, 1.8]. The zero values represent dBIS points. d Time-averaged spin texture by discretizing the momentum space k_x, k_y ∈ [−1.8, 1.8] into a 15 × 15 lattice, where the dBIS momenta can be outlined according to the zero values. The black dot and green dashed line correspond to the case of a, b and c, respectively. e Dynamical field g = (g_x, g_y) (black arrows) obtained from the time-averaged spin texture. Here we set w_x = 0.05ξ₀, w_y = 0, w_z = 0.01ξ₀, and ξ_so = 0.2ξ₀.