Ordered droplets in quantum magnets with long-range interactions

TL;DR

This paper investigates how long-range interactions affect droplet formation in quantum magnets near criticality, finding that such interactions do not prevent droplet nucleation for large defects.

Contribution

It provides a theoretical analysis of droplet formation in quantum magnets with long-range interactions using Landau-Ginzburg-Wilson theory, highlighting the subleading role of power-law tails.

Findings

Long-range interactions cause power-law tails in droplets.

For $\sigma>0$, tails are subleading for large droplets.

Droplet formation remains feasible despite long-range interactions.

Abstract

A defect coupling to the square of the order parameter in a nearly quantum-critical magnet can nucleate an ordered droplet while the bulk system is in the paramagnetic phase. We study the influence of long-range spatial interactions of the form $r^{-(d+\sigma)}$ on the droplet formation. To this end, we solve a Landau-Ginzburg-Wilson free energy in saddle point approximation. The long-range interaction causes the droplet to develop an energetically unfavorable power-law tail. However, for $\sigma>0$, the free energy contribution of this tail is subleading in the limit of large droplets; and the droplet formation is controlled by the defect bulk. Thus, for large defects, long-range interactions do not hinder the formation of droplets.