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Demystifying the holographic mystique: A critical review

Khveshchenko

Published Apr 18, 2020• 0 citations
Publisher

Abstract

Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various ‘strange’ metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).

DOI
10.17615/5mde-tr96

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various ‘strange’ metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).
A tour guide of holographic matter A quake is rumbling through the core of physics. Suddenly apparently unrelated areas appear to have a common ground, showing an eerie capacity to fertilise each other. In physics such occasions are invariably propelled by novel mathematical machinery and the present case is no exception. This new mathematical contraption is “holographic duality” (or “anti-de Sitter/conformal field theory correspondence”), which was originally discovered in string theory in the 1990s. Until recently its use was limited to the historic scope of string theory – particle physics and quantum gravity. At a breathtaking pace it has since rolled out over many of the subject areas of modern fundamental physics, even yielding new insights into old subjects such as the nineteenth-century theory of hydrodynamics. Several books of this kind could be written, and are being written, highlighting how anti-de Sitter/conformal field theory (AdS/CFT) impacts on various fields in physics. This book will focus on a prominent area where the developments have been particularly stunning. This is the application to equilibrium condensed matter physics. This started in 2007, and in a matter of a few years condensed matter theory was rewritten in a different mathematical language. This language is the one that one would perhaps least expect: general relativity. On its own a rewriting of condensed matter might not sound like a great advance, no matter how unconventional the language. However, the correspondence makes it possible to explore regimes of quantum many-body physics that are completely inaccessible with conventional techniques. In particular we refer to non-Fermi-liquid states of matter formed in finite-density systems of strongly interacting fermion systems. The holographic mathematics here becomes particularly expressive, suggesting that a general principle of a new kind is at work. It appears that this principle relates to the physics of compressible quantum matter: the notion that the nature of this state of matter is governed by a macroscopic quantum entanglement involving allof its constituents. This discovery is not just remarkable on its own. “Holographic strange matter” also has tantalisingly suggestive resemblances to the mysterious phenomena observed experimentally in strongly interacting electron systems that have been realised in special materials such as the high-T c superconductors. First seen around thirty years ago, these have defied any reasonable explanation despite countless attempts resting on the available mathematical techniques.
I begin with a review of quantum impurity models in condensed matter physics, in which a localized spin degree of freedom is coupled to an interacting conformal field theory in \\(d\\) = 2 spatial dimensions. Their properties are similar to those of supersymmetric generalizations which can be solved by the AdS/CFT correspondence; the low energy limit of the latter models is described by a \\(AdS_2\\) geometry. Then I turn to Kondo lattice models, which can be described by a mean- field theory obtained by a mapping to a quantum impurity coupled to a self-consistent environment. Such a theory yields a 'fractionalized Fermi liquid' phase of conduction electrons coupled to a critical spin liquid state, and is an attractive mean-field theory of strange metals. The recent holographic description of strange metals with a \\(AdS_2 \\times R^2\\) geometry is argued to be related to such mean-field solutions of Kondo lattice models.
Liu replies: While many ingenious ideas have been advanced to explain the strange-metal phase, the community has not reached a consensus, and many of the phase’s properties remain mysterious. Philip W. Anderson’s hidden Fermi liquid theory, arguably a most ambitious attempt, has provided a useful lens to view various aspects of the phase, but further developments are worthwhile.As described in my Quick Study, a key obstacle in the pursuit to explain the strange metal phase is the lack of a suitable mathematical framework to characterize “quantum soups”—strongly interacting, dense quantum matter whose constituents have lost their individuality. Holographic duality has now provided such a framework, although only for the class of systems that have gravity duals. It does for those quantum soups what Boltzmann equations do for a dilute gas of quasiparticles: It enables one to calculate reliably all equilibrium and nonequilibrium properties.At short distances, holographic systems are conformal, Lorentz invariant, and often supersymmetric, all of which make them seem poor models for real-life condensed-matter systems. Those symmetries, however, are all destroyed at long distances if a temperature or a chemical potential is turned on. The surprise of the past few years is that despite significant differences in short-distance details, at long distances most states of matter that have been understood—superfluids, Fermi liquids, magnets, stripes, and so on—can be described in terms of dual gravity systems. Such insensitivity to microscopic detail gives hope that the striking parallels in macroscopic behavior found between black holes and strange metals are not accidents, and gravity may help us decipher the mysteries of strange metals.I thank Anderson for emphasizing other anomalies exhibited by the strange-metal phase of cuprates that I did not have space to mention. He is correct that the holographic approach has not yet produced a model that could account for all anomalous properties. However, the power-law dependence of photoemission spectra on energy, his last bullet point, is a hallmark of holographic strange metals. I discussed that point in the last part of the Quick Study, in terms of the power-law temperature dependence of scattering rates. Such power laws follow from the semilocal property emphasized in the second-to-last paragraph.Whether or not one finds a “conventional” explanation for strange metals, connections between the physics of strange metals and black holes are worth exploring. They hint at a new paradigm for thinking about strongly correlated quantum soups. As an added bonus, we may also obtain new insights into quantum gravity from advances in condensed-matter physics.© 2013 American Institute of Physics.
Abstract This is a review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)‐Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s‐, p‐ or d‐wave holographic superconductors and “electron stars”. Finally we present a realization of local quantum criticality with an impurity problem.