How Generic Scale Invariance Influences Quantum and Classical Phase Transitions
TL;DR: In this article, the authors discuss a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of order parameter only.
Abstract: This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.
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TL;DR: In this paper, the physical properties of transition-metal-based ferromagnets have been studied and the Curie-Weiss behavior at high temperature is replaced by the critical susceptibility just above the curie temperatures, which are 47.9 K and 25.6 K, respectively.
Abstract: We present a report on the physical properties of the transition-metal-based ferromagnets ${\mathrm{HfFeGa}}_{2}$ and ${\mathrm{HfMnGa}}_{2}$. The magnetic susceptibility in both displays Curie-Weiss behavior at high temperature that is replaced by the critical susceptibility just above the Curie temperatures, which are 47.9 K in ${\mathrm{HfFeGa}}_{2}$ and 25.6 K in ${\mathrm{HfMnGa}}_{2}$. The ferromagnetically ordered state has a coercive field of 1700 Oe in ${\mathrm{HfFeGa}}_{2}$ and 320 Oe in ${\mathrm{HfMnGa}}_{2}$, with strong anisotropy that largely confines the moments to the $b$ axis. Critical exponents that are derived from neutron diffraction measurements and Arrott plot analyses of the magnetization confirm the mean-field character of the ferromagnetic transitions. Phonons dominate the specific heat at all temperatures, but clear ordering anomalies accompany the onset of ferromagnetic order, as well as an electronic component that is larger in the ordered than paramagnetic states. Both ${\mathrm{HfFeGa}}_{2}$ and ${\mathrm{HfMnGa}}_{2}$ are metallic, and we observe an anomalous exponent in the temperature-dependent resistivity $\ensuremath{\rho}(T)$, where $\ensuremath{\rho}(T)\ensuremath{-}{\ensuremath{\rho}}_{0}={\mathit{BT}}^{5/3}$, signaling that the ordered state is a marginal Fermi liquid. Overall, the robustness of ferromagnetic order, the Curie temperatures, and the impact of fluctuations in both ${\mathrm{HfFeGa}}_{2}$ and ${\mathrm{HfMnGa}}_{2}$ are very similar to those of previously studied ferromagnets, such as MnSi, ZrZn${}_{2}$, Ni${}_{3}$Al, and Sc${}_{3}$In.
5 citations
TL;DR: In this article, the magnetic analogs of superconductivity are considered as candidate states for the hidden order that sometimes develops in the vicinity of quantum critical points in metallic systems, which can be thought of as "pairing" in the particle-hole channel and are tabulated.
Abstract: This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revisited and refreshed in new materials, new probes, and new theoretical ideas. New universality and apparent zero temperature phases of matter move us beyond the old ideas of quantum criticality. This is accompanied by alternative pairing interactions and as yet unidentified phases developing in the vicinity of quantum critical points. In discussing novel order, the magnetic analogs of superconductivity are considered as candidate states for the hidden order that sometimes develops in the vicinity of quantum critical points in metallic systems. These analogs can be thought of as "pairing" in the particle-hole channel and are tabulated. This analogy is used to outline a framework to study the relation between ferromagnetic fluctuations and the propensity of a metal to nematic type phases - which at weak coupling correspond to Pomeranchuk instabilities. This question can be related to the fundamental relations of Fermi liquid theory.
5 citations
TL;DR: In this paper, a muon spin relaxation was found to exhibit power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly.
Abstract: We report results of a muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) study of ${\mathrm{YFe}}_{2}{\mathrm{Al}}_{10}$, a quasi-two-dimensional (2D) nearly ferromagnetic metal in which unconventional quantum critical behavior is observed. No static ${\mathrm{Fe}}^{2+}$ magnetism, with or without long-range order, is found down to 19 mK. The dynamic muon spin relaxation rate $\ensuremath{\lambda}$ exhibits power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly. We attribute this to the proportionality of $\ensuremath{\lambda}({\ensuremath{\omega}}_{\ensuremath{\mu}},T)$ to the dynamic structure factor $S({\ensuremath{\omega}}_{\ensuremath{\mu}},T)$, where ${\ensuremath{\omega}}_{\ensuremath{\mu}}\ensuremath{\approx}{10}^{5}\ensuremath{-}{10}^{7}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ is the muon Zeeman frequency. These results suggest critical divergences of $S({\ensuremath{\omega}}_{\ensuremath{\mu}},T)$ in both temperature and frequency. Power-law scaling and a 2D dissipative quantum XY model both yield forms for $S(\ensuremath{\omega},T)$ that agree with neutron scattering data ($\ensuremath{\omega}\ensuremath{\approx}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$). Extrapolation to $\ensuremath{\mu}\mathrm{SR}$ frequencies agrees semiquantitatively with the observed temperature dependence of $\ensuremath{\lambda}({\ensuremath{\omega}}_{\ensuremath{\mu}},T)$, but predicts frequency independence for ${\ensuremath{\omega}}_{\ensuremath{\mu}}\ensuremath{\ll}T$, in extreme disagreement with experiment. We conclude that the quantum critical spin dynamics of ${\mathrm{YFe}}_{2}{\mathrm{Al}}_{10}$ is not well understood at low frequencies.
5 citations
TL;DR: In this article, a wide class of quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to a topological insulator or a Chern insulator.
Abstract: We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to a topological insulator or a Chern insulator. Changes in Fermi-surface topology concomitant with [SU(2) or time-reversal] symmetry breakings generate quantum critical lines (QCLs) even beyond the quantum critical point. This QCL running at temperature $T=0$ separates two distinct topological phases. This is in contrast to the simple termination of the finite-temperature critical line at the quantum critical point without any extension of it at $T=0$. Topology change causes the unconventionality beyond the concept of simple spontaneous symmetry breaking assumed in the conventional Landau-Ginzburg-Wilson scenario. The unconventional universality implied by mean-field critical exponents $\ensuremath{\beta}g1/2$ and $\ensuremath{\delta}l3$ is protected by the existence of the quantum critical line. It emerges for several specific lattice models including the honeycomb, kagome, diamond, and pyrochlore lattices. We also clarify phase diagrams of the topological phases in these lattices at finite temperatures.
5 citations
TL;DR: In this article, the authors give a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions, and point out the computational challenges posed by quantum phase transition.
Abstract: This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.
5 citations
References
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Book•
01 Jan 1972
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Abstract: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies. Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.
12,039 citations
Book•
01 Feb 1974
TL;DR: In this paper, the authors define an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures and describe the properties of these mixtures.
Abstract: Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-, quasi-long and short-range order remarkable features of liquid crystals. Part 2 Long- and short-range order in nematics: definition of an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures. Part 3 Static distortion in a nematic single crystal: principles of the continuum theory magnetic field effects electric field effects in an insulating nematic fluctuations in the alignment hydrostatics of nematics. Part 4 Defects and textures in nematics: observations disclination lines point disclinations walls under magnetic fields umbilics surface disclinations. Part 5 Dynamical properties of nematics: the equations of "nematodynamics" experiments measuring the Leslie co-efficients convective instabilities under electric fields molecular motions. Part 6 Cholesterics: optical properties of an ideal helix agents influencing the pitch dynamical properties textures and defects in cholesterics. Part 7 Smectics: symmetry of the main smectic phases continuum description of smectics A and C remarks on phase and precritical phenomena.
9,683 citations
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Abstract: A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.
7,090 citations
TL;DR: In this paper, it is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic.
Abstract: It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.
6,236 citations
30 Jun 1995
TL;DR: Weinberg as discussed by the authors presented a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics, including supersymmetric algebras.
Abstract: In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.
4,988 citations