Singular dynamics and emergence of nonlocality in long-range quantum models

TL;DR

This paper investigates how nonlocality arises and influences the dynamics in long-range quantum models, revealing singular modes that cause deviations from locality and impact system behavior after quenches.

Contribution

It introduces the concept of singular modes in long-range quantum systems and analyzes their effects on dynamics, static correlations, and conformal invariance.

Findings

Identification of two dynamic behaviors in long-range systems

Relation of singular modes to power-law decay tails

Impact of singular modes on conformal invariance breakdown

Abstract

We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of the equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent \alpha). By studying the dynamic correlation functions, we find that for every finite \alpha two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes, having in general energies far from the minima of the spectrum, where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to "singular" modes, and as to "singular dynamics" to their dynamics. For the Kitaev model they are manifest, at finite \alpha, in derivatives of the quasiparticle energy, the order of the derivative at which the singularity occurs increasing with \alpha. The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.