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.
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TL;DR: Etude de verres de spin d'Ising a ordre a courte distance a n dimensions avec dynamique de renversement de spin locale: la f onction de correlation aurait pour limite inferieure une fonction de la forme exp.
Abstract: Etude de verres de spin d'Ising a ordre a courte distance a n dimensions avec dynamique de renversement de spin locale: la fonction de correlation aurait pour limite inferieure une fonction de la forme exp. [−c(log t) d/d−1 ] aux temperatures superieures a celle de la transition verre de spin, la relaxation lente de grands amas isoles de spins non frustres etant responsables de cette limite. Possibilite d'une phase de Griffiths entre verre de spin et phase paramagnetique
165 citations
TL;DR: In this paper, momentum-shell recursion relations for classical fixed-length spins in 2 + ε 2 + √ √ ε ϵ 2 dimensions were constructed.
Abstract: We describe in detail how to construct momentum-shell recursion relations for classical fixed-length spins in $d=2+\ensuremath{\epsilon}$ dimensions. The theory is then applied to anisotropic spin systems and to a model of nematic liquid crystals. We also develop a trajectory-integral formalism, which is used to produce the free energy, magnetization, and susceptibilities of isotropic spin systems to first order in $\ensuremath{\epsilon}=d\ensuremath{-}2$.
163 citations
TL;DR: In this paper, it was shown that the pairing spectrum of excitations giving superconductivity is not that normally associated with a proximity to quantum criticality in weak itinerant ferromagnets.
Abstract: in t he pressure dependence of the static susceptibility. This demonstrates that the spectrum of excitations giving superconductivity is not that normally associated with a proximity to quantum criticality in weak itinerant ferromagnets. In contrast our data suggest that instead the pairing spectrum might be related to a sharp spike in the electronic density of states that also drives one of the magnetic transitions. PACS numbers: 71.27.+2, 74.70.Tx, 75.50.Cc The possible co-existence of superconductivity and ferromagnetism, although considered as a theoretical possibility for idealised weak itinerant ferromagnets over 20 years ago [1,2] has only recently been demonstrated to occur experimentally [3{5]. The theoretical calculations assumed the superconductivity to be mediated by an abundance of low-energy small-wavevector magnetic excitations. These excitations become prevalent near a ferromagnetic quantum critical point (QCP), that is at the value of the pressure (or another control parameter) at which a second order transition is driven to zero temperature and at which the longitudinal magnetic susceptibility becomes singular. More recent theoretical work suggests that in an isotropic material a coupling between transverse and longitudinal excitations, which is present only in the ferromagnetic phase, should give a much higher superconducting transition in the ferromagnetic state [6]. The presence of crystalline anisotropy has also been considered, and was shown to circumvent the depression of the superconducting critical temperature exactly at the QCP itself [7]. For UGe2 it has already been established that in the limit of zero temperature the transition from ferromagnetism to paramagnetism as the pressure is increased through pc 15:8kbar is
162 citations
TL;DR: The universal dynamic and static properties of two-dimensional antiferromagnets in the vicinity of a zero-temperature phase transition from long-range magnetic order to a quantum-disordered phase are studied.
Abstract: The universal dynamic and static properties of two-dimensional antiferromagnets in the vicinity of a zero-temperature phase transition from long-range magnetic order to a quantum-disordered phase are studied. Random antiferromagnets with both N\'eel and spin-glass long-range magnetic order are considered. Explicit quantum-critical dynamic scaling functions are computed in a 1/N expansion to two-loop level for certain nonrandom, frustrated square-lattice antiferromagnets. Implications for neutron scattering experiments on the doped cuprates are noted.
160 citations
TL;DR: The renormalization group treatment of metamagnetic quantum criticality in metals is presented, showing that for clean systems the universality class is that of the overdamped, conserving, Ising type.
Abstract: We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ except very near to the critical point itself.
160 citations