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

Abstract

We study the role of long-range interactions on the non-equilibrium dynamics considering a long-range Kitaev chain in which superconducting term decays with distance between two sites in a power-law fashion characterised 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 quenching of the chemical potential (μ) across a quantum critical point, depends non-trivially on the exponent α as long as α<2; on the other hand, for α>2, one finds that the exponent saturates to the corresponding well-know value of 1/2 expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the non-analyticities 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.