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: The renormalizability of this model in two dimensions and its ultraviolet asymptotic freedom are used to derive renormalization-group equations valid above $d = 2.
Abstract: The long-distance properties of classical Heisenberg ferromagnets below the transition point are related to a continuous-field theory, the nonlinear $\ensuremath{\sigma}$ model. The renormalizability of this model in two dimensions and its ultraviolet asymptotic freedom are used to derive renormalization-group equations valid above $d=2$. It is argued that this model is renormalizable up to four dimensions. The scaling properties which incorporate critical and Goldstone singularities follow. Explicit calculations of exponents and of correlation functions in powers of $d\ensuremath{-}2$ are given. A technique is proposed to make calculations in the symmetric phase applicable even in two dimensions.
425 citations
01 Jan 2002
TL;DR: In this article, the static scaling laws, which have the objective of reducing the number of independent critical exponents to a couple, are discussed. But their justification was later found later in the renormalization program.
Abstract: We begin with the static scaling laws which have the objective of reducing the number of independent critical exponents to a couple, and the proposal is to achieve this by focussing on ever smaller neighborhoods of the critical point. The basic ideas of scaling are to be traced back to [Essam and Fisher, 1963, Widom, 1965, Kadanoff, 1966, Fisher, 1967a]; their justification was found later in the renormalization program we discuss in the next section. In a nutshell, the idea was that in the neighborhood of the critical point, the thermodynamic functions can be assumed to be generalized homogenous functions; see e.g. [Stanley, 1971, Fisher, 1983, Cardy, 1996].
418 citations
TL;DR: In this paper, strong anisotropies and nonlinearities of the longitudinal resistivity ρxx were observed at the ground state or first excited Landau level but begin abruptly in the third level.
Abstract: Magnetotransport experiments on high mobility two-dimensional electron gases in GaAs/AlGaAs heterostructures have revealed striking anomalies near half filling of several spin-resolved, yet highly excited, Landau levels. These anomalies include strong anisotropies and nonlinearities of the longitudinal resistivity ρxx which commence only below about 150 mK. These phenomena are not seen in the ground state or first excited Landau level but begin abruptly in the third level. Although their origin remains unclear, we speculate that they reflect the spontaneous development of a generic anisotropic many-electron state.
414 citations
TL;DR: In this article, the specific heat and electrical resistivity of the heavy-fermion alloy (CeCu) 5.9 were measured over more than a decade in temperature T. The magnetic susceptibility measured in 0.1 T showed a cusp for T ≥ 0.
Abstract: The specific heat C and electrical resistivity \ensuremath{\rho} of the heavy-fermion alloy ${\mathrm{CeCu}}_{5.9}$${\mathrm{Au}}_{0.1}$ exhibit non-Fermi-liquid behavior well below 1 K, i.e., C/T\ensuremath{\propto}-ln(T/${\mathit{T}}_{0}$) and \ensuremath{\rho}=${\mathrm{\ensuremath{\rho}}}_{0}$+A'T, over more than a decade in temperature T. The magnetic susceptibility \ensuremath{\chi} measured in 0.1 T shows a cusp for T\ensuremath{\rightarrow}0. This behavior is attributed to the proximity to magnetic order: In contrast to ${\mathrm{CeCu}}_{6}$, ${\mathrm{CeCu}}_{6\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Au}}_{\mathit{x}}$ alloys show long-range antiferromagnetic order, with ${\mathit{T}}_{\mathit{N}}$\ensuremath{\rightarrow}0 for ${\mathit{x}}_{\mathit{c}}$=0.1. Hence ${\mathrm{CeCu}}_{5.9}$${\mathrm{Au}}_{0.1}$ is at the edge of a zero-temperature quantum phase transition. In a large magnetic field (B\ensuremath{\ge}3 T) Fermi-liquid behavior is recovered.
405 citations
TL;DR: The observation of superconductivity in the ferromagnetically ordered phase of the d-electron compound ZrZn2 suggests that metallic ferromagnets may universally become superconducting when the magnetization is small.
Abstract: It has generally been believed that, within the context of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, the conduction electrons in a metal cannot be both ferromagnetically ordered and superconducting. Even when the superconductivity has been interpreted as arising from magnetic mediation of the paired electrons, it was thought that the superconducting state occurs in the paramagnetic phase. Here we report the observation of superconductivity in the ferromagnetically ordered phase of the d-electron compound ZrZn2. The specific heat anomaly associated with the superconducting transition in this material appears to be absent, and the superconducting state is very sensitive to defects, occurring only in very pure samples. Under hydrostatic pressure superconductivity and ferromagnetism disappear at the same pressure, so the ferromagnetic state appears to be a prerequisite for superconductivity. When combined with the recent observation of superconductivity in UGe2 (ref. 4), our results suggest that metallic ferromagnets may universally become superconducting when the magnetization is small.
358 citations