Exciton-driven quantum phase transitions in holography

We study phase transitions driven by fermionic double-trace deformations in gauge-gravity duality. Both the strength of the double trace deformation and the infrared conformal dimension/self-energy scaling of the quasiparticle can be used to decrease the critical temperature to zero, leading to a line of quantum critical points. The self-energy scaling is controlled indirectly through an applied magnetic field and the quantum phase transition naturally involves the condensation of a fermion bilinear which models the spin density wave in an antiferromagnetic state. The nature of the quantum critical points depends on the parameters and we find either a Berezinskii-Kosterlitz-Thouless-type transition or one of two distinct second order transitions with non-mean field exponents. One of these is an anomalous branch where the order parameter of constituent non-Fermi liquid quasiparticles is enhanced by the magnetic field. Stabilization of ordered non-Fermi liquids by a strong magnetic field is observed in experiments with highly oriented pyrolytic graphite.Comment: 44 pages, 16 figures; published versio

Holographic non-relativistic fermionic fixed point and bulk dipole coupling

Inspired by the recently discovered non-relativistic fermionic fixed points, we investigate how the presence of bulk dipole coupling modifies the spectral function at one of these novel fixed points. As a result, although the infinite flat band is always visible in the presence of the bulk dipole coupling as well as chemical potential, the band is modified in a remarkable way at small momenta up to the order of magnitude of bulk dipole coupling. On the other hand, like a phoenix, a new Fermi surface sprouts from the formed gap when the bulk dipole coupling is pushed up further such as to overshadow the charge parameter, which is obviously different from what is found at the relativistic fixed points.Comment: JHEP style, 1+17 pages, 9 figures, 1 table, typos corrected, references added, version to appear in JHE

Constructing the AdS dual of a Fermi liquid: AdS black holes with Dirac hair

Theoretical Physic

Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality

We study lattice effects in strongly coupled systems of fermions at a finite density described by a holographic dual consisting of fermions in Anti-de-Sitter space in the presence of a Reissner-Nordstrom black hole. The lattice effect is encoded by a periodic modulation of the chemical potential with a wavelength of order of the intrinsic length scales of the system. This corresponds with a highly complicated "band structure" problem in AdS, which we only manage to solve in the weak potential limit. The "domain wall" fermions in AdS encoding for the Fermi surfaces in the boundary field theory diffract as usually against the periodic lattice, giving rise to band gaps. However, the deep infrared of the field theory as encoded by the near horizon AdS2 geometry in the bulk reacts in a surprising way to the weak potential. The hybridization of the fermions bulk dualizes into a linear combination of CFT1 "local quantum critical" propagators in the bulk, characterized by momentum dependent exponents displaced by lattice Umklapp vectors. This has the consequence that the metals showing quasi-Fermi surfaces cannot be localized in band insulators. In the AdS2 metal regime, where the conformal dimension of the fermionic operator is large and no Fermi surfaces are present at low T/\mu, the lattice gives rise to a characteristic dependence of the energy scaling as a function of momentum. We predict crossovers from a high energy standard momentum AdS2 scaling to a low energy regime where exponents found associated with momenta "backscattered" to a lower Brillioun zone in the extended zone scheme. We comment on how these findings can be used as a unique fingerprint for the detection of AdS2 like "pseudogap metals" in the laboratory.Comment: 42 pages, 5 figures; v2, minor correction, to appear in JHE

Holographic models for undoped Weyl semimetals

We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2. We present new results for the spectral densities and dispersion relations at non-zero momenta and temperature. In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential. Our findings show that the boundary system behaves like an undoped Weyl semimetal.Comment: 64 pages, 19 figure

Holographic Aspects of Fermi Liquids in a Background Magnetic Field

We study the effects of an external magnetic field on the properties of the quasiparticle spectrum of the class of 2+1 dimensional strongly coupled theories holographically dual to charged AdS$_4$ black holes at zero temperature. We uncover several interesting features. At certain values of the magnetic field, there are multiple quasiparticle peaks representing a novel level structure of the associated Fermi surfaces. Furthermore, increasing magnetic field deforms the dispersion characteristics of the quasiparticle peaks from non-Landau toward Landau behaviour. At a certain value of the magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid, the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed non-separable solutions to infinite-sum solution

Friedel Oscillations in Holographic Metals

In this article we study the conditions under which holographic metallic states display Friedel oscillations. We focus on systems where the bulk charge density is not hidden behind a black hole horizon. Understanding holographic Friedel oscillations gives a clean way to characterize the boundary system, complementary to probe fermion calculations. We find that fermions in a "hard wall" AdS geometry unambiguously display Friedel oscillations. However, similar oscillations are washed out for electron stars, suggesting a smeared continuum of Fermi surfaces.Comment: 26 pages, 5 figure

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.Comment: 31 pages, 7 figure

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

Driven by the landscape of garden-variety condensed matter systems, we have investigated how the dual spectral function behaves at the non-relativistic as well as relativistic fermionic fixed point by considering the probe Dirac fermion in an extremal charged dilatonic black hole with zero entropy. Although the pattern for both of the appearance of flat band and emergence of Fermi surface is qualitatively similar to that given by the probe fermion in the extremal Reissner-Nordstrom AdS black hole, we find a distinctly different low energy behavior around the Fermi surface, which can be traced back to the different near horizon geometry. In particular, with the peculiar near horizon geometry of our extremal charged dilatonic black hole, the low energy behavior exhibits the universal linear dispersion relation and scaling property, where the former indicates that the dual liquid is a Fermi one while the latter implies that the dual liquid is not exactly of Landau Fermi type

Striped instability of a holographic Fermi-like liquid

We consider a holographic description of a system of strongly-coupled fermions in 2+1 dimensions based on a D7-brane probe in the background of D3-branes. The black hole embedding represents a Fermi-like liquid. We study the excitations of the Fermi liquid system. Above a critical density which depends on the temperature, the system becomes unstable towards an inhomogeneous modulated phase which is similar to a charge density and spin wave state. The essence of this instability can be effectively described by a Maxwell-axion theory with a background electric field. We also consider the fate of zero sound at non-zero temperature.Comment: 16 pages, 9 figures; v2: added discussion and one figure. Typos correcte