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      Non-Fermi liquids from holography

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          Abstract

          We report on a potentially new class of non-Fermi liquids in (2+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.

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          Building an AdS/CFT superconductor

          Gary T. Horowitz, Christopher Herzog, Sean Hartnoll (2008)
          We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (DC) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.
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            Renormalization Group Approach to Interacting Fermions

            R. Shankar (1993)
            The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to \(\phi^4\) theory in four dimensions and the path integral formulation for fermions is given. The strategy is as follows. First, the modes on either side of the Fermi surface within a cut-off \(\Lambda\) are chosen and a path integral is written to describe them. An RG transformation which eliminates a part of these modes, but preserves the action of the noninteracting system is identified. Finally the possible perturbations of this free-field fixed point are classified as relevant, irrelevant or marginal. A \(d=1\) warmup calculation involving a system of fermions shows how, in contrast to mean-field theory, the RG correctly yields a scale invariant system (Luttinger liquid) In \(d=2\) and 3, for rotationally invariant Fermi surfaces, {\em automatically} leads to Landau's Fermi liquid theory, which appears as a fixed point characterized by an effective mass and a Landau function \(F\), with the only relevant perturbations being of the superconducting (BCS) type The functional flow equations for the BCS couplings are derived and separated into an infinite number of flows, one for each angular momentum. It is shown that similar results hold for rotationally non-invariant (but time-reversal invariant) Fermi surfaces also, A study of a nested Fermi surface shows an additional relevant flow leading to charge density wave formation. For small \(\Lambda / K_F\), a 1/N expansion emerges, with \(N = K_F/ \Lambda\), which explains why one is able to solve the narrow cut-off theory. The search for non-Fermi liquids in \(d=2\)
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              Singular Fermi Liquids

              C. M. VARMA, W. van Saarloos, Z. Nussinov (2001)
              An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi liquids) include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of Singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues highlighted.
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                Author and article information

                Journal
                Publication date Created: 16 March 2009
                Publication date Updated: 2009-07-16
                Article
                DOI: 10.1103/PhysRevD.83.065029
                ArXiV ID: 0903.2477
                SO-VID: ab696b34-6dd1-4b97-84a9-b4f840575542
                License:

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Report No MIT-CTP/4023
                Journal reference Phys.Rev.D83:065029,2011
                Comments 10 pages, 16 figures. v2: added references, corrected figures, some minor changes. v3: figure 5 replaced
                Categories hep-th cond-mat.str-el

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