Interplay between short-range and critical long-range fluctuations in the out-of-equilibrium behavior of the particle density at quantum transitions

TL;DR

This paper investigates how short-range and critical long-range quantum fluctuations influence the out-of-equilibrium particle density near quantum transitions, using the Kitaev chain model to reveal dynamic scaling behaviors.

Contribution

It provides a detailed analysis of out-of-equilibrium particle density scaling at quantum critical points, highlighting the interplay of different fluctuation regimes in a well-studied model.

Findings

Identification of out-of-equilibrium scaling behaviors of particle density

Demonstration of the interplay between short-range and long-range fluctuations

Application of dynamic finite-size scaling framework to quantum quenches

Abstract

We address the equilibrium and out-of-equilibrium behavior of the particle density in many-body systems undergoing quantum transitions driven by the chemical potential $\mu$. They originate from a nontrivial interplay between noncritical short-range and critical long-range quantum fluctuations. As a paradigmatic model we consider the one-dimensional fermionic Kitaev chain, for which very accurate numerical studies can be performed, up to $O(10^4)$ sites. The search for dynamic scaling behaviors of the particle density is complicated by the fact that its equilibrium (ground state) behavior is dominated by short-range fluctuations, giving rise to regular background terms and peculiar logarithmic terms from resonances between renormalization-group perturbations associated with the energy and identity operator families within the conformal field theory. To study these issues, we focus on two dynamic protocols, either instantaneous quenches or quasi-adiabatic changes of $\mu$ to the critical value $\mu_c$, unveiling out-of-equilibrium scaling behaviors of the particle density, which arise from the critical modes, within a dynamic finite-size scaling framework.