Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Abstract Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems. We study the topological and dynamical properties of the quasiperiodic Su–Schrier–Heeger model with long-range hoppings. It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with non-zero winding numbers ω = 1 , 2 , and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length. We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths. The critical exponents extracted from the dynamical behavior agree with the Kibble–Zurek mechanic prediction for the path with W = 0.90 . In particular, the dynamical exponent of the path crossing the multicritical point is numerical obtained as 1 / 6 ∼ 0.167 , which agrees with the unconventional finding in the previously studied XY spin model. Besides, we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.