Quantum ferromagnetic transition in disordered itinerant electron systems

Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions liste...

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the cross-over between diffusive and ballistic regimes of quantum interference effects occurs at a temperature $ T^{\ast}=1/\tau \gamma (E_{F}\tau)^{2}$, where $\gamma $ is the parameter associated with the Landau damping of the spin fluctuation...

We calculate the temperature dependence of conductivity due to interaction correction for a disordered itinerant electron system close to a ferromagnetic quantum critical point which occurs due to a spin density wave instability. In the quantum critical regime, the crossover between diffusive and ballistic transport occurs at a temperature $T^{\ast}=1/[\tau \gamma (E_{F}\tau)^{2}]$, where $\gamma$ is the parameter associated with the Landau damping of the spin fluctuations, $...

The zero temperature, or quantum, metal-superconductor phase transition is studied in disordered systems in dimension greater than two. A effective local field theory is developed that keeps all soft modes or fluctuations explicitly. A simple renormalization group analysis is used to exactly determine the quantum critical behavior at this transition.

Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder driven semimetal to metal quantum phase transition of three dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical an...

A comprehensive theory for electronic transport in itinerant ferromagnets is developed. We first show that the Q-field theory used previously to describe a disordered Fermi liquid also has a saddle-point solution that describes a ferromagnet in a disordered Stoner approximation. We calculate transport coefficients and thermodynamic susceptibilities by expanding about the saddle point to Gaussian order. At this level, the theory generalizes previous RPA-type theories by includ...

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 $z=2 +{\rm O}(\epsilon^2)$ in the sense of $\epsilon$ expansion, as previously discovered in the Ising limit. It appears, however,...

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effecti...

We present a detailed analysis of the non-analytic structure of the free energy for the itinerant ferromagnet near the quantum critical point in two and three dimensions. We analyze a model of electrons with an isotropic dispersion interacting through a contact repulsion. A fermionic version of the quantum order-by-disorder mechanism allows us to calculate the free energy as a functional of the dispersion in the presence of homogeneous and spiralling magnetic order. We re-sum...

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The main concepts relating to quantum phase transitions are explained, using the paramagnet-to-ferromagnet transition of itinerant electrons as the primary example. Some aspects of metal-insulator transitions are also briefly discussed. The exposition is strictly pedagogical in nature, with no ambitions with respect to completeness or going into technical details. The ...