Quantum Griffiths effects in itinerant Heisenberg magnets

TL;DR

This paper investigates how quenched disorder affects quantum phase transitions in itinerant Heisenberg magnets, revealing strong Griffiths singularities near the critical point, contrasting with the Ising case.

Contribution

It demonstrates the presence of power-law Griffiths singularities in Heisenberg systems and provides explicit calculations for O(N) models, expanding understanding of disorder effects.

Findings

Heisenberg magnets exhibit strong Griffiths singularities near quantum critical points.

Explicit large-N calculations support the scaling arguments.

Implications for classifying quantum phase transitions with disorder.

Abstract

We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the overdamping suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we illustrate them by an explicit calculation for O(N) spin symmetry in the large-N limit. We also discuss broad implications for the classification of quantum phase transitions in the presence of quenched disorder.