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, it has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and a charged scalar.
Abstract: It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar We review our earlier analysis of this theory and extend it in two directions First, we consider all values for the charge of the scalar field Away from the large charge limit, backreaction on the spacetime metric is important While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found We go on to add a perpendicular magnetic field B and obtain the London equation and magnetic penetration depth We show that these holographic superconductors are Type II, ie, starting in a normal phase at large B and low temperatures, they develop superconducting droplets as B is reduced
1,059 citations
TL;DR: In this paper, the authors summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticalities and the interplay between quantum criticalness and unconventional superconductivity.
Abstract: Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity. At a zero-temperature phase transition from one ordered state to another, fluctuations between the two states lead to quantum critical behaviour that can lead to unexpected physics. Metals with ‘heavy’ electrons often harbour such weird states.
1,055 citations
TL;DR: In this article, the authors review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors.
Abstract: We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.
668 citations
TL;DR: The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed in this paper, where superconductivity has been found at the border of magnetic order as well as deep within ferromagnetic and antiferromagnetically ordered states.
Abstract: Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.
529 citations
TL;DR: The functional renormalization group as discussed by the authors is a flexible and unbiased tool for dealing with scale-dependent behavior of correlated fermion systems, such as Luttinger liquid behavior and the Kondo effect.
Abstract: Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems; (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals; and (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and nonequilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. A self-contained derivation of the exact flow equations is presented and frequently used truncation schemes are described. Reviewing selected applications it is shown how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.
511 citations
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TL;DR: In this article, the authors extend the application of the mode-coupling theory for the dynamics of critical fluctuations in fluids into the non-asymptotic critical region, which incorporates the crossover from asymptotic singular behavior near critical point to the regular behavior of these transport properties far away from the critical point, and compare experimental data for the thermal diffusivity, the thermal conductivity, and the viscosity of carbon dioxide and ethane.
Abstract: We extend the application of the mode‐coupling theory for the dynamics of critical fluctuations in fluids into the non‐asymptotic critical region. An approximate solution of the mode‐coupling equations yields a set of representative equations for the thermal conductivity and the viscosity of one‐component fluids which incorporates the crossover from asymptotic singular behavior near the critical point to the regular behavior of these transport properties far away from the critical point. The equations for the critical enhancements of the thermal conductivity and the viscosity depend on the background transport properties of the fluid, the equilibrium thermodynamic properties of the fluid, and one fluid‐dependent wave‐number cutoff qD, which is indicative of the crossover length scale. We compare our crossover model with experimental data for the thermal diffusivity, the thermal conductivity, and the viscosity of carbon dioxide and ethane.
82 citations
TL;DR: In this article, the authors studied the spin-spin correlation functions and showed that the average value and second moment of the temperature derivatives of these correlations are infinitely differentiable but fail to be analytic at the temperature at which the observable specific heat fails to be analyzed.
Abstract: We continue our investigation of an Ising model with immobile random impurities by studying the spin-spin correlation functions. These correlations are not probability-1 objects and have a probability distribution. When the random bonds have the particular distribution function studied in the first paper of this series, we demonstrate that the average value and the second moment of the temperature derivatives of these correlations are infinitely differentiable but fail to be analytic at ${T}_{c}$, the temperature at which the observable specific heat fails to be analytic. When $Tl{T}_{c}$, we consider ${S}_{\ensuremath{\infty}}(l)=limit of\text{}〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{l,m}〉\text{as}m\ensuremath{\rightarrow}\ensuremath{\infty}$. This limit is not independent of $l$. In the special case that the random bonds are symmetrically distributed about the $l$th row, the geometric mean of ${S}_{\ensuremath{\infty}}(l)$ is computed and shown to vanish exponentially rapidly when $T\ensuremath{\rightarrow}{T}_{c}\ensuremath{-}$. We contrast this with a lower bound that shows that the spontaneous magnetization can vanish no more rapidly than ${T}_{c}\ensuremath{-}T$, and present a description of how the local magnetization ${S}_{\ensuremath{\infty}}{(l)}^{\frac{1}{2}}$ behaves as $T\ensuremath{\rightarrow}{T}_{c}\ensuremath{-}$.
79 citations
TL;DR: Nonperturbative contributions are shown to produce anomalously slow relaxation in dilute ferromagnets (or antiferromagnet) both in the paramagnetic and ``Griffiths'' phases.
Abstract: Nonperturbative contributions are shown to produce anomalously slow relaxation in dilute ferromagnets (or antiferromagnets), both in the paramagnetic and ``Griffiths'' phases. In the paramagnetic phase, the pseudoscaling form C(t)\ensuremath{\sim}exp{-${\mathit{t}}^{\mathit{d}/(\mathit{d}+\mathit{z})}$f(t/${\ensuremath{\xi}}_{\mathit{p}}^{\mathit{d}+\mathit{z}}$)} is predicted for the spin autocorrelation function, with ${\ensuremath{\xi}}_{\mathit{p}}$ the correlation length of the nondilute system. In the Griffiths phase, C(t)\ensuremath{\sim}exp{-A1nt${)}^{\mathit{d}/(\mathit{d}\mathrm{\ensuremath{-}}1)}$} and exp{-(Bt${)}^{1/2}$} are predicted for Ising Heisenberg systems, respectively, for t\ensuremath{\gg}${\ensuremath{\xi}}_{\mathit{p}}^{\mathit{d}+\mathit{z}}$.
79 citations
74 citations
01 Jan 1983
TL;DR: In this article, the de Gennes model is used as a basis for a discussion of the properties of the nematic and smectic-A phases and the transition between them.
Abstract: The de Gennes model is used as a basis for a discussion of the properties of the nematic and smectic-A phases and the transition between them. Order parameter and director correlation functions and the Landau-Peierls destruction of long range order in the smectic phase are reviewed. A gauge transformation that restores long range order to the smectic phase is introduced. Anisotropic scaling with correlation length exponents, ν|| and ν┴ , is presented and shown to imply that the critical point in three dimensions with finite splay elastic constant must either be isotropic (ν|| = ν┴ ) and in the same universality class as the superconducting transition or anisotropic with ν|| = 2ν┴ . Predictions for the behavior of physically measurable quantities for these two universality classes are presented and compared with experiment. Predictions for both classes are in agreement with some but not all experiments.
72 citations