Physics and Astronomy Calendar

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 whether one can introduce an order parameter and construct a controllable expansion in it near the QCP, what are the "correct" fermionic and bosonic modes at criticality, and whether the Hertz theory -- the "standard model" of quantum critical behavior, is actually correct. I argue that a controllable, Eliashberg-type expansion at QCP is possible, and can be rigorously justified. I further show that for an SU(2) -
symmetric ferromagnetic QCP, there exists singular corrections to spin susceptibility, which are not present in the Hertz theory. These singularities destroy a ferromagnetic QCP and (depending on parameters) either lead to first order transition, or to intermediate spiral phase. Similar effect also exists near an antiferromagnetic QCP. There it does not destroy a continuous transition, but still leads to an anomalous behavior of the dynamic spin susceptibility.