Transport phenomena and correlation dynamics of a one-dimensional effective Hamiltonian equivalent to the hexagonal Harper model

The phase diagram of the one-dimensional hexagonal Harper (HH) model reveals the presence of two metallic phases and one insulating phase, separated by critical lines and a bicritical point. In our work, we investigate transport in the different phases by considering both the isolated and open system scenario. For the case of the isolated system, we study the single -particle dynamics at the bicritical point and along the critical lines. We find that the single -particle wave packet dynamics is superdiffusive in the critical regions with the transport at the bicritical point faster than that along the critical lines. In addition, we study domain wall (DW) dynamics via unconventional multiparticle states in the two metallic phases. The DW state is constructed by partially filling half of the chain while the other half is kept empty; the dynamics of this state reveals distinct behavior in the deep metallic regime of the two metallic phases. Interestingly, the distinct behavior is absent if one instead considers a fully filled half chain. For the open system scenario, we study transport in the nonequilibrium steady state (NESS). We observe that in the critical regions, transport is subdiffusive in nature. Moreover, we find that the transport scaling exponents for the open system scenario are the same at the bicritical point and along the critical lines, unlike the closed system case. In addition, we observe an even -odd size effect on the NESS density and current and on the optimal system -bath coupling parameter (corresponding to the maximum current) in the deep metallic regime of the HH model.