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arXiv:cond-mat/0401149 · Physical Review Letters

Ferromagnetic Transition in One-Dimensional Itinerant Electron Systems

Kun Yang

Published Aug 3, 2004• 45 citations
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Abstract

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.

DOI
10.1103/physrevlett.93.066401

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We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.
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)z=2+\mathrm{O}({ϵ}^{2})z=2+O(ϵ2) in the sense of ϵϵϵ 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)G(x,t=0)G(x,t=0) and G(x=0,t)G(x=0,t)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 study the magnetic behavior of an itinerant, strongly interacting fermion system for varying values of the coupling constant and for arbitrary dimensionalities 1<d< 31<d<~31<d< 3. We show that, at zero temperature, due to quantum effects, the critical exponents are the mean-field ones below two dimensions as well as above. We then focus on the critical behavior of the two-dimensional case, which, within some assumptions that are discussed, exhibits a ferromagnetic rather than antiferromagnetic character. We also compute the effects of critical fluctuations on the lowtemperature properties of such systems.
A comprehensive theory of the quantum phase transition in clean itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions d< 3d<~3d< 3 due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension dc+=3.{d}_{\mathrm{c}\mathrm{}}^{+}=3.dc+​=3. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition and of the critical behavior at the fluctuation-induced second-order transition. In d=3,d=3,d=3, the latter is mean field like with logarithmic corrections to scaling, and in d<3d<3d<3 it can be controlled by means of a $3\ensuremath{-}\ensuremath{\epsilon}$ expansion.
Based on phase space arguments, we develop a simple approach to metallic quantum critical points, designed to study the problem without integrating the fermions out of the partition function. The method is applied to the spin-fermion model of a T=0T=0T=0 ferromagnetic transition. Stability criteria for the conduction and the spin fluids are derived by scaling at the tree level. We conclude that anomalous exponents may be generated for the fermion self-energy and the spin--spin correlation functions below d=3,d=3,d=3, in spite of the spin fluid being above its upper critical dimension.