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 $α\to 2$.