| A ferromagnetic quantum criticality
Andrey Chubukov
Department of Physics, University of Wisconsin Madison
I consider the problem of 2D fermions interacting with gapless long-wavelength collective
bosonic modes. The theory describes, among other cases, a ferromagnetic quantum-critical
point (QCP) and a QCP towards nematic ordering. There have been intensive discussions
recently about what is the form of the fermionic propagator at criticality, and whether the
Hertz φ4 theory – the “standard model” of quantum critical behavior, is correct. I argue
that controllable calculations at QCP are possible, despite that fermionic propagator has
a non-Fermi liquid form. I further show that for an SU(2) symmetric ferromagnetic QCP,
the φ4 model is incorrect as φ4 and higher-order vertices contain singular dynamical terms
originating from backscattering. These singularities destroy a continuous ferromagnetic
QCP and, depending on the parameters, either lead to a first order transition, or to an
intermediate spiral phase. I show that a similar effect also exists near an antiferromagnetic
QCP. It does not destroy a continuous transition, but leads to the anomalous exponent for
the dynamic spin susceptibility.
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