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

## TL;DR

This paper investigates how long-range interactions influence the non-equilibrium dynamics of a long-range Kitaev chain, revealing a dependence of the Kibble-Zurek scaling and dynamical phase transitions on the decay exponent of interactions.

## Contribution

It demonstrates the non-trivial dependence of the Kibble-Zurek scaling exponent on the long-range interaction decay exponent and identifies a new region of dynamical quantum phase transitions.

## Key findings

- Kibble-Zurek exponent varies with interaction range for α<2
- For α>2, the exponent saturates to 1/2, matching short-range models
- A new region with three cusp singularities in the rate function is identified

## 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 $\alpha$. 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 ($\mu$) across a quantum critical point, depends non-trivially on the exponent $\alpha$ as long as $\alpha <2$; on the other hand, for $\alpha >2$, 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 $\mu$, 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 $\alpha$ increases and vanishes in the limit $\alpha \to 2$.