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 spin-fermion model near the antiferromagnetic instability in two dimensions was analyzed and it was shown that λ scales with the spin correlation length and diverges at criticality, implying that the conventional perturbative expansion breaks down.
Abstract: We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms...
355 citations
TL;DR: In this paper, the pair correlation between spins considered at different times in a ferromagnetic crystal is used to derive a general formula for the angular and energy distribution of magnetically scattered neutrons.
Abstract: The pair correlation between spins considered at different times in a ferromagnetic crystal is used to derive a general formula for the angular and energy distribution of magnetically scattered neutrons. The qualitative properties of the correlation are established for various temperature ranges and a number of characteristic features of the scattering and of its temperature variation are thus accounted for. From the study of the long-range part of the correlation an explicit expression is derived for the "critical magnetic scattering" produced in the neighborhood of the Curie point by the large spontaneous fluctuations of the magnetization.
349 citations
TL;DR: In this article, a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions was developed, and explicit expressions for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the director wave) is overdamped except along special directions dictated by symmetry.
Abstract: We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the director wave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of $z=3,$ implying stability of the Gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi-liquid theory in the nematic phase and to strongly angle-dependent electronic self energies around the Fermi surface. Other metallic liquid-crystal phases, e.g., a quantum hexatic, behave analogously.
344 citations
TL;DR: In this article, a method is developed which allows the evaluation of the closed formal expressions for electrical conductivity which have recently been developed by several authors, and a brief mention of the application of this method to liquids and alloys is made.
Abstract: A method is developed which allows the evaluation of the closed formal expressions for electrical conductivity which have recently been developed by several authors. The case of a random set of scatterers is treated in detail and the formal solution made to yield directly the solution to the Boltzmann equation. A brief mention of the application of this method to liquids and alloys is made.
341 citations
TL;DR: Spontaneous dimerization was found in the isotropic Heisenberg antiferromagnetic chain with competing nearest-and next-nearest-neighbor exchange, and results from the same umklapp processes that lead to the N\'eel state when easy-axis exchange anisotropy is present as mentioned in this paper.
Abstract: Spontaneous dimerization is found in the $S=\frac{1}{2}$ isotropic Heisenberg antiferromagnetic chain with competing nearest- and next-nearest-neighbor exchange, $\frac{{J}_{2}}{{J}_{1}}\ensuremath{\gtrsim}\frac{1}{6}$, and results from the same umklapp processes that lead to the N\'eel state when easy-axis exchange anisotropy is present. Spontaneous and externally induced dimerizations are contrasted.
337 citations