One-dimensional itinerant ferromagnets with Heisenberg symmetry and the ferromagnetic quantum critical point

TL;DR

This paper investigates the quantum critical behavior of one-dimensional itinerant ferromagnets with Heisenberg symmetry, highlighting the role of Berry phase terms and providing exact electron Green functions for experimental insights.

Contribution

It introduces the effect of Berry phase in the SU(2) symmetric case and discusses the different universality class from the Ising limit, with explicit calculations of Green functions.

Findings

Berry phase term appears with SU(2) symmetry

Dynamical critical exponent is approximately 2

Exact electron Green functions are derived

Abstract

We study one-dimensional itinerant ferromagnets with Heisenberg symmetry near a ferromagnetic quantum critical point. It is shown that the Berry phase term arises in the effective action of itinerant ferromagnets when the full SU(2) symmetry is present. We explicitly demonstrate that dynamical critical exponent of the theory with the Berry term is $z=2 +{\rm O}(\epsilon^2)$ in the sense of $\epsilon$ expansion, as previously discovered in the Ising limit. It appears, however, that the universality class at the interacting fixed point is not the same. We point out that even though the critical theory in the Ising limit can be obtained by the standard Hertz-Millis approach, the Heisenberg limit is expected to be different. We also calculate the exact electron Green functions $G(x,t=0)$ and $G(x=0,t)$ near the transition in a range of temperature, which can be used for experimental signatures of the associated critical points.