We study one-dimensional itinerant ferromagnets with Heisenberg symmetry near a ferromagnetic quantum critical point. It is shown that the Berry phase term arises in the effective action of itinerant ferromagnets when the full SU(2) symmetry is present. We explicitly demonstrate that dynamical critical exponent of the theory with the Berry term is
z=2+O(ϵ2) in the sense of
ϵ expansion, as previously discovered in the Ising limit. It appears, however, that the universality class at the interacting fixed point is not the same. We point out that even though the critical theory in the Ising limit can be obtained by the standard Hertz-Millis approach, the Heisenberg limit is expected to be different. We also calculate the exact electron Green functions
G(x,t=0) and
G(x=0,t) near the transition in a range of temperature, which can be used for experimental signatures of the associated critical points.
We show that spin-
S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small
S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an
S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.