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arXiv:cond-mat/0209190 · Physical review. B, Condensed matter

Nature of the quantum phase transition in clean itinerant Heisenberg ferromagnets

T. R. Kirkpatrick, D. Belitz

Published Jan 22, 2003• 47 citations
arXivHTMLPDF

Abstract

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 $d<~3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension ${d}_{\mathrm{c}\mathrm{}}^{+}=3.$ 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 $d=3,$ the latter is mean field like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3\ensuremath{-}\ensuremath{\epsilon}$ expansion.

DOI
10.1103/physrevb.67.024419

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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 listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
We describe the quantum phase transitions in the ferromagnetic Dicke-Ising model using a Landau theory approach. The theory quantitatively captures the change from a second- to a first-order transition between the normal and superradiant phases through a tricritical point. We identify virtual nearest-neighbor double spin-flip processes as the crucial mechanism responsible for this behavior. The tricritical point constitutes a quantum phase transition above the upper critical dimension. We discuss the modifications to finite-size scaling required for the correct interpretation of numerical data at the tricritical point. Our results emphasize the need for adapted finite-size scaling forms in all-to-all interacting quantum systems and establish the ferromagnetic Dicke-Ising model as a paradigmatic platform for quantum phase transitions above the upper critical dimension, encompassing both standard φ4φ^4φ4 criticality and beyond.
The purpose of this work is to understand the zero temperature phases and the phase transitions of Heisenberg spin systems which can have an extensive, spontaneous magnetic moment; this entails a study of quantum transitions with an order parameter which is also a non-abelian conserved charge. To this end, we introduce and study a new class of lattice models of quantum rotors. We compute their mean-field phase diagrams and present continuum, quantum field-theoretic descriptions of their low energy properties in different regimes. We argue that, in spatial dimensiond=1, the phase transitions in itinerant Fermi systems are in the same universality class as the corresponding transitions in certain rotor models. We discuss implications of our results for itinerant fermions systems in higherdand for other physical systems.
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The phase-ordering dynamics that results from domain coarsening is considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase, there appears a transient regime where the domain growth follows a different power law than in the classical case, and for asymptotically long times, the prefactor of the t1∕2{t}^{1∕2}t1∕2 growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.