Holographic Metals and the Fractionalized Fermi Liquid

Abstract

We show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a 'small' Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at non-zero density realizing the near-horizon, AdS2×R 2 physics of Reissner-Nordström black holes.There has been a flurry of recent activity [1-10] on the holographic description of metallic states of non-zero density quantum matter. The strategy is to begin with a strongly interacting conformal field theory (CFT) in the ultraviolet (UV), which has a dual description as the boundary of a theory of gravity in anti-de Sitter (AdS) space. This CFT is then perturbed by a chemical potential (µ) conjugate to a globally conserved charge, and the infrared (IR) physics is given a holographic description by the gravity theory. For large temperatures T ≫ µ, such an approach is under good control, and has produced a useful hydrodynamic description of the physics of quantum criticality [11]. Much less is understood about the low temperature limit T ≪ µ: a direct solution of the classical gravity theory yields boundary correlation functions describing a non-Fermi liquid metal [4], but the physical interpretation of this state has remained obscure. It has a non-zero entropy density as T → 0, and this raises concerns about its ultimate stability. This paper will show that there is a close parallel between the above theories of holographic metals, and a class of mean-field theories of the 'fractionalized Fermi liquid' (FFL) phase of the lattice Anderson model. The Anderson model (specified below) has been a popular description of inter-metallic transition metal or rareearth compounds: it describes itinerant conduction electrons interacting with localized resonant states representing d (or f ) orbitals. The FFL is an exotic phase of the Anderson model, demonstrated to be generically stable in Refs. [12,13]: it has a 'small' Fermi surface whose volume is determined by the density of conduction electrons alone, while the d electrons form a fractionalized spin liquid state. The FFL was also found in a large spatial dimension mean field theory by Burdin et al. [14], and is the ground state needed for a true "orbital-selective Mott transition" [15]. The FFL should be contrasted from the conventional Fermi liquid phase (FL), in which there is a 'large' Fermi surface whose volume counts both the conduction and d electrons: the FL phase is the accepted description of many 'heavy fermion' rare-earth intermetallics. However, recent experiments on YbRh 2 (Si 0.95 Ge 0.05 ) 2 have observed an unusual phase for which the FFL is an attractive candidate [16].Here, we will describe the spin liquid of the FFL by the gapless mean-field state of Sachdev and Ye [17] (SY). We will then find that physical properties of the ...

Fermi surfaces and gauge-gravity duality

“…Specifically [74], both models had compressible phases with non-zero ground state entropy density, correlations which had momentum-independent singular temporal correlations with the structure of conformal quantum mechanics, and singular damping of the gauge-neutral particles at the c Fermi surface. It was proposed [22], therefore, that the gravity theory of Ref. 6 had realized an infinite-range limit of the FL* phase.…”

“…Nevertheless, it is quite remarkable that two very different solvable limits lead to essentially the same physical properties, which could apply to physical systems over a significant interme-diate energy scale [22].…”

“…Clearly, a proper condensed matter interpretation of these putative states is urgently needed. [22,23] A. The Luttinger Theorem This theorem was originally established for a gas of fermions with weak or moderate interactions.…”

Remarks on the Sachdev-Ye-Kitaev model

“…It is a simple variant of a model introduced by Sachdev and Ye [4], which was first discussed in relation to holography in [5]. The Hamiltonian of [1] is simply…”

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

“…It is even ambiguous to define a non-Fermi liquid, although possible deviations from Fermi liquid theory include, for example, violation of Luttinger's 7 famed volume theorem, vanishing quasiparticle weight, and/or anomalous thermodynamics and transport. 5,[8][9][10][11][12] This theoretical quandary is rather unfortunate as it is likely prohibiting a full understanding of the mechanism behind high-temperature superconductivity, as well as stymying theoretically-guided searches for new exotic materials.Pioneering early theoretical work on the cuprates relied on two main premises, 3,13-17 from which we will be guided but not constrained in our pursuit and understanding of a particular non-Fermi liquid metal: (1) that the microscopics can be described by the square lattice Hubbard model with on-site Coulomb repulsion, which at strong coupling reduces in its simplest form to the t-J model; and (2) that the physics of the system can be faithfully represented by the "slave-boson" technique, wherein the physical electron operator is written as a product of a slave boson ("chargon"), which carries the electronic charge, and a spin-1/2 fermionic "spinon," 18 which carries the spin, both strongly coupled to an emergent gauge field. However, within the slave-boson formulation, it has been difficult to access non-Fermi liquid physics at low temperatures because this requires the chargons to be in an uncondensed, yet conducting, quantum phase, 19 i.e., some sort of the elusive "Bose metal."…”