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Journal ArticleDOI

Interaction-driven localization in holography

01 Oct 2013-Nature Physics (Nature Research)-Vol. 9, Iss: 10, pp 649-655
TL;DR: In this paper, a periodic lattice was introduced to a holographic model developed by string theorists to study anisotropic materials that are insulating in certain directions but conducting in others.
Abstract: Strongly interacting condensed-matter systems are often computationally intractable. By introducing a periodic lattice to a holographic model developed by string theorists, it becomes possible to study anisotropic materials that are insulating in certain directions but conducting in others.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a holographic model consisting of Einstein-Maxwell theory in d + 1 bulk spacetime dimensions with d 1 massless scalarelds was considered, and the DC conductivity was analytically calculated.
Abstract: We consider a holographic model consisting of Einstein-Maxwell theory in d + 1 bulk spacetime dimensions with d 1 massless scalarelds. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which isnite. In the d = 3 case, both the black hole geometry and shear-mode current- current correlators are those of a sector of massive gravity.

519 citations


Cites background from "Interaction-driven localization in ..."

  • ...This is similar in spirit to constructions in 5 bulk dimensions where Bianchi VII0 symmetry can be exploited to construct helical black holes through the solution of ODEs rather than PDEs [17]....

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Book
16 Mar 2018
TL;DR: In this paper, a review of theories of states of quantum matter without quasiparticle excitations is provided through a holographic duality with gravitational theories in an emergent spatial dimension.
Abstract: We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

484 citations


Cites background or methods from "Interaction-driven localization in ..."

  • ...32 Spectral weight transfer: Optical conductivity in the metallic (left) and insulating (right) phases of the model from [226]....

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  • ...If the dimension νkL of the lattice deformation in the low energy compressible phase can be continuously tuned at T = 0 from being irrelevant to relevant – for instance by varying the charge density at fixed lattice wavevector – then a metal-insulator transition results [226]....

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  • ...The zero temperature limit of the fully backreacted solution exhibits an emergent anisotropic IR scaling symmetry with entropy density vanishing like s ∼ T 2/3 [226]....

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  • ...Gapless holographic insulators were constructed in [58; 215; 224; 226; 291; 295]....

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  • ...This physics allows for anisotropic systems that are insulating in one direction but conductive in another [226]....

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Journal ArticleDOI
TL;DR: In this article, the authors introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance, which leads to constructions that involve solving ODEs instead of PDEs.
Abstract: We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS 3 × $ \mathbb{R} $ solution.

379 citations

Journal ArticleDOI
TL;DR: In this paper, an analytic expression for the DC electrical conductivity in terms of black hole horizon data was obtained for a class of holographic Q-lattices exhibiting momentum dissipation.
Abstract: An analytic expression for the DC electrical conductivity in terms of black hole horizon data was recently obtained for a class of holographic black holes exhibiting momentum dissipation. We generalise this result to obtain analogous expressions for the DC thermoelectric and thermal conductivities. We illustrate our results using some holographic Q-lattice black holes as well as for some black holes with linear massless axions, in both D = 4 and D = 5 bulk spacetime dimensions, which include both spatially isotropic and anisotropic examples. We show that some recently constructed ground states of holographic Q-lattices, which can be either electrically insulating or metallic, are all thermal insulators.

323 citations


Cites background from "Interaction-driven localization in ..."

  • ...(2)For the special case of D= 5, helical lattices can also be constructed by solving ODEs [15], extending [16, 17]....

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  • ...2For the special case of D = 5, helical lattices can also be constructed by solving ODEs [15], extending [16,17]....

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  • ...This is a significant technical simplification since the black holes can be constructed by solving ODEs instead of PDEs2 as in the constructions [15, 18–22]....

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Journal ArticleDOI
TL;DR: In this paper, the authors examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars, and analyze the possible IR phases in terms of various scaling exponents and the importance of operators in the IR effective holographic theory with a dilaton.
Abstract: In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilaton. We compute the (finite) resistivity and encounter broad families of (in)coherent metals and insulators, characterized by universal scaling behaviour. The optical conductivity at zero temperature and low frequencies exhibits power tails which can violate scaling symmetries, due to the running of the dilaton. At low temperatures, our model captures features of random-field disorder.

303 citations


Cites background or result from "Interaction-driven localization in ..."

  • ...If the resistivity diverges at low temperatures, we find soft-gapped insulators, which have a translation-invariant metric and no anisotropy contrarily to those of [28, 29]....

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  • ...Another interesting setup could involve helical (Bianchi VII) symmetries, [28]....

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  • ...3), contrarily to hyperscaling cases [14, 22, 28]: this is a side effect of a strong running of the dilaton, happening in regions of the parameter space where the exponents ζ and κλ (or alternatively, the gauge- and axiondilaton couplings) governing the AC conductivity are unbounded....

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  • ...On the other hand, if the resistivity blows up at zero temperature, the system behaves like a soft-gapped insulator (earlier examples of which can be found in [28, 29]), with # > 0 in (1....

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  • ...Note that differently to [28, 29], these insulators are characterized by isotropic gravity duals, which in particular means that lower-dimensional IR boundaries are not a necessary ingredient of holographic insulators (as in [28])....

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References
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Journal ArticleDOI
TL;DR: A review of the metal-insulator transition can be found in this article, where a pedagogical introduction to the subject is given, as well as a comparison between experimental results and theoretical achievements.
Abstract: Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

5,781 citations

Journal ArticleDOI
TL;DR: In this paper, a prescription for computing Minkowski-space correlators from AdS/CFT correspondence was formulated and shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in two dimensions.
Abstract: We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature = 4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.

1,478 citations

Journal ArticleDOI
TL;DR: This work discusses black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space, and reviews Myers-Perry solutions, black rings, and solution-generating techniques.
Abstract: We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

860 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by ''Lorentz''-invariant quantum critical points was presented.
Abstract: We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by ``Lorentz''-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field $B$, and a deviation in the density $\ensuremath{\rho}$ from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a ``hydrodynamic cyclotron mode'' which could be observable in ultrapure samples. We also present exact results for the zero frequency transport coefficients of a supersymmetric conformal field theory (CFT), which is solvable by the anti--de Sitter (AdS)/CFT correspondence. This correspondence maps the $\ensuremath{\rho}$ and $B$ perturbations of the $2+1$ dimensional CFT to electric and magnetic charges of a black hole in the $3+1$ dimensional anti--de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

662 citations