$z = 3$ antiferromagnetic quantum criticality and emergence of fermionized skyrmions

TL;DR

This paper demonstrates a transition from z=2 to z=3 in antiferromagnetic quantum criticality due to long-range interactions, highlighting the emergence of fermionized skyrmions forming a Fermi surface.

Contribution

It introduces a dual field theory showing how fermionized skyrmions lead to z=3 criticality, extending understanding beyond the traditional Hertz-Moriya-Millis framework.

Findings

Critical exponent shifts from z=2 to z=3 at low temperatures.

Fermionized skyrmions form a Fermi surface, creating a skyrmion liquid.

Dual field theory captures the emergent fermionized skyrmion physics.

Abstract

Hertz-Moriya-Millis theory with dynamical critical exponent $z = 2$ has been proposed to describe antiferromagnetic quantum criticality in itinerant electron systems. In this study we show that the dynamical critical exponent changes from $z = 2$ to $z = 3$ at low temperatures, which results from effective long-range interactions between spin fluctuations, generated by Fermi-surface fluctuations beyond the Eliashberg framework. We claim that the underlying physics for the $z = 3$ antiferromagnetic quantum criticality is the emergence of fermionized skyrmion excitations at low energies, which form a Fermi surface, referred as a skyrmion liquid, where the interplay between itinerant electrons and skyrmions is argued to allow fermionized skyrmions. We construct a dual field theory in terms of skyrmion excitations, and obtain the $z = 3$ antiferromagnetic quantum criticality. This demonstration suggests the expected but nontrivial consistency between weak-coupling and strong-coupling theories.