Approximate light cone effects in a non-relativistic quantum field theory after a local quench

TL;DR

This paper investigates how correlations spread in a non-relativistic quantum field theory after a local quench, revealing light cone effects with a width growing as the square root of time, despite unbounded dispersion.

Contribution

It provides an exact asymptotic analysis of correlation spreading in non-relativistic fermions, showing light cone effects with superluminal corrections and extending results to trapped systems.

Findings

Correlation spreading exhibits light cone effects with width ∝ t^{1/2}.

Superluminal corrections dominate over pure light cone behavior.

Results extend to systems with harmonic trapping and multiple joins.

Abstract

We study the spreading of correlations after a local quench in a non-relativistic quantum field theory. We focus on noninteracting non-relativistic fermions and study the time evolution after two identical systems in their ground states are suddenly joined together with a localized impurity at the junction. We find that, even if the quasi-particles of the system have unbounded dispersion, the correlations show light cone effects. We carry out a detailed study of these effects by developing an accurate asymptotic expansion of the two-point function and determining exactly the density of particles at any time after the quench. In particular, we find that the width of the light cone region is $\propto t^{1/2}$. The structure of correlations, however, does not show a pure light cone form - "superluminal corrections" are much larger than in the bounded-dispersion case. These findings can be explained by inspecting the structure of excitations generated by the initial state. We show that a similar picture also emerges in the presence of a harmonic trapping potential and when more than two systems are suddenly joined at a single point.