Quantum field theory of metallic spin glasses

TL;DR

This paper develops an effective field theory for quantum phase transitions in metallic spin glasses, revealing the dominance of static disorder fluctuations and the irrelevance of quantum dynamics near criticality.

Contribution

It introduces a static disorder-focused field theory for quantum spin glass transitions, with a renormalization-group analysis showing stability conditions and scaling hypotheses.

Findings

Critical properties are dominated by static disorder fluctuations.

Dynamic quantum effects are dangerously irrelevant at the transition.

Scaling hypotheses suggest a static strong-coupling critical field theory.

Abstract

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.