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Holography, fermi surfaces and criticality

Mihailo Čubrović

Published Feb 27, 2013• 0 citations
OpenAlex

Abstract

We employ the novel method of AdS/CFT correspondence to study strongly correlated fermions, their ground states and the phase transitions between them. AdS/CFT maps the quantum many-body problem to a classical gravity problem, making it more tractable. We find a holographic description of Fermi liquids and then proceed to find novel non-Fermi liquid ground states. In the future one can expect AdS/CFT to contribute toward our understanding of real world materials

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We employ the novel method of AdS/CFT correspondence to study strongly correlated fermions, their ground states and the phase transitions between them. AdS/CFT maps the quantum many-body problem to a classical gravity problem, making it more tractable. We find a holographic description of Fermi liquids and then proceed to find novel non-Fermi liquid ground states. In the future one can expect AdS/CFT to contribute toward our understanding of real world materials
A central problem in quantum condensed matter physics is the critical theory governing the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi-liquid.
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.
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 an 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 an AdS 2 × R 2 geometry is argued to be related to such mean-field solutions of Kondo lattice models.
We report on a potentially new class of non-Fermi liquids in (2+12+12+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.
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.
This paper addresses the problem of computing fermion propagators in a broad variety of strongly correlated systems that can be mapped onto the theory of fermions coupled to an (over)damped bosonic mode. A number of the previously applied approaches and their results are reviewed, including the conventional diagrammatic resummation and eikonal technique, as well as the ‘experimental’ higher-dimensional bosonization and generalized (i.e. ‘bottom-up’ or ‘non-AdS/non-CFT’) holographic conjecture. It appears that, by and large, those results remain either in conflict or incomplete, thereby suggesting that the ultimate solution to this ubiquitous problem is yet to be found.