The Study of Topological Phase Transition of One-Dimensional Disordered Su-Schrieffer-Heeger Model

Here we investigate the topological phase transition of a general one-dimensional (1D) disordered Su–Schrieffer–Heeger (SSH) model, with two tunable parameters, the disorder distribution center ξ and a dimensionless ratio k between the disorder strengths of the intracell and intercell hopping terms. First, for each realization or the ensemble average, we numerically observe a topological phase transition (TPT) with quantized real-space winding number jump and disappearing of zero-energy edge states when the disorder strength increases. Second, surprisingly, we find that the critical point of TPT is determined by the equality between the geometry means of intracell and intercell hopping terms. Third, a new theory based on the redefined sublattices is developed, which proves that the critical condition of TPT of the 1D disordered model is governed by the equality of the products of odd and even hopping terms and agrees with our numerical results. The theory also shows that the sudden change picture of TPT, not the gradual inverse picture, is correct, and that the origin of TPT is from the sub-symmetry of the model. Fourth, other models with different parameters are also studied. The TPTs of these models also follow our theoretical predictions. These results contribute to a better understanding of TPTs in 1D disordered systems.