Quantum field theory of metallic spin glasses

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{≤}8. Scaling hypotheses for a static strong-coupling critical field theory are proposed. The nonlinear 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.