Probing the role of long-range interactions in the dynamics of a long-range Kitaev chain

We study the role of long-range interactions (more precisely, the long-range superconducting gap term) on the nonequilibrium dynamics considering a long-range p-wave superconducting chain in which the superconducting term decays with distance between two sites in a power-law fashion characterized by an exponent α. We show that the Kibble-Zurek scaling exponent, dictating the power-law decay of the defect density in the final state reached following a slow (in comparison to the time scale associated with the minimum gap in the spectrum of the Hamiltonian) quenching of the chemical potential μ across a quantum critical point, depends nontrivially on the exponent α as long as α<2; on the other hand, for α>2, we find that the exponent saturates to the corresponding well-known value of $1/2$ expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the nonanalyticities in the rate function of the return possibility $I(t)$ in subsequent temporal evolution following a sudden change in μ, we show the existence of a new region; in this region, we find three instants of cusp singularities in $I(t)$ associated with a single sector of Fisher zeros. Notably, the width of this region shrinks as α increases and vanishes in the limit α→2, indicating that this special region is an artifact of the long-range nature of the Hamiltonian.