We present a top-down string theory holographic model of strongly interacting relativistic 2+1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe $D7$-branes in $AdS_5 \times S^5$, stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at one-loop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory.
In electronic systems with flat bands, such as twisted bilayer graphene, interaction effects govern the structure of the phase diagram. In this paper, we show that a strongly interacting system featuring fermionic flat bands can be engineered using the holographic duality. In particular, we find that in the holographic nematic phase, two bulk Dirac cones separated in momentum space at low temperature, approach each other as the temperature increases. They eventually collide at a critical temperature yielding a flattened band with a quadratic dispersion. On the other hand, in the symmetric (Lif…
Using holographic methods we investigate the behaviour of fermionic spectral functions of strongly coupled 2+1 dimensional field theories as both temperature and chemical potential are quenched.
In this paper, we apply the K-theory scheme of classifying the topological insulators/superconductors to classify the topological classes of the massive multi-flavor fermions in anti-de Sitter (AdS) space. In the context of AdS/CFT correspondence, the multi-flavor fermionic mass matrix is dual to the pattern of operator mixing in the boundary conformal field theory (CFT). Thus, our results classify the possible patterns of operator mixings among fermionic operators in the holographic CFT.
We discuss Holographic Renormalization Group equations in the presence of fermions and form fields in the bulk. The existence of a holographically dual quantum field theory for a given bulk gravity theory imposes consistency conditions on the ranks of the form fields, the fermion - form field couplings, and leads to a novel Ward identity.
In this letter, we systematically explore the holographic (non-)relativistic fermionic spectrum without/with dipole coupling dual to Born-Infeld anti-de Sitter (BI-AdS) black hole. For the relativistic fermionic fixed point, this holographic fermionic system exhibits non-Fermi liquid behavior. Also, with the increase of BI parameter $γ$, the non-Fermi liquid becomes even "more non-Fermi". When the dipole coupling term is included, we find that the BI term makes it a lot tougher to form the gap. While for the non-relativistic fermionic system with large dipole coupling in BI-AdS background, wit…
We study the ferminoic spectrum with Weyl correction, which exhibits the non-Fermi liquid behavior. Also, we find that both the height of the peak of the fermionic spectrum and the dispersion relation exhibit a nonlinearity with the variety of the Weyl coupling parameter $γ$, which mean that such nonlinearity maybe ascribe to the one of the Maxwell field. Another important property of this system is that for the holographic fermionic system with $γ<0$, the degree of the deviation from Fermi liquid is heavier than that for the one with $γ>0$. It indicates that there is a transition of coupling …
In this work we initiate the study of open effective field theories of fermions interacting with holographic baths. As a first step in this direction, we explain how the recently identified holographic Schwinger-Keldysh saddles naturally reproduce the Fermi-Dirac statistics of boundary correlators. We study Dirac fermions propagating in the background of a doubled $AdS_{d+1}$ Schwarzchild blackbrane. We solve for both ingoing (quasi-normal) as well as outgoing (Hawking) modes of the Dirac field in a boundary gradient expansion and compare our findings against exact results in $d=2$. The hologr…
We consider a holographic fermionic system in which the fermions are interacting with a U(1) gauge field in the presence of a dilaton field in a gravity bulk of a charged black hole with hyperscaling violation. Using both analytical and numerical methods, we investigate the properties of the infrared and ultaviolet Green's functions of the holographic fermionic system. Studying the spectral functions of the system, we find that as the hyperscaling violation exponent is varied, the fermionic system possesses Fermi, non-Fermi, marginal-Fermi and log-oscillating liquid phases. Various liquid phas…
We study the interface between a fractional topological insulator and an ordinary insulator, both described using holography. By turning on a chemical potential we induce a finite density of matter localized at the interface. These are gapless surface excitations which are expected to have a fermionic character. We study the thermodynamics of the system, finding a symmetry preserving compressible state at low temperatures, whose excitations exhibit hyperscaling violation. These results are consistent with the expectation of gapless fermionic excitations forming a Fermi surface at finite densit…
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 overs…
We investigate the holographic fermions over a gravitational lattice background with a rather low temperature. Since the rotation symmetry is broken on the plane, the lattice effects change the shape of the Fermi surface within the first Brillouin zone from a circle to an ellipse. When the Fermi surface intersects with the Brillouin zone boundary, the band structure with a band gap is observed through a numerical analysis. We construct a lattice model sourced by a scalar field as well as an ionic lattice model without the scalar field. In both cases we find the similar physical results.
We use holography to compute spectral functions of certain fermionic operators in three different finite-density, zero-temperature states of ABJM theory with a broken U(1) symmetry. In each of the three states, dual to previously studied domain wall solutions of four-dimensional gauged supergravity, we find that the fermionic operators have gapped spectra. In one case the gap can be traced to the small charge of the fermions, while in the other cases it is due to a particular interaction that mixes particles and holes.
We study the fermionic spectral density in a strongly correlated quantum system described by a gravity dual. In the presence of periodically modulated chemical potential, which models the effect of the ionic lattice, we explore the shapes of the corresponding Fermi surfaces, defined by the location of peaks in the spectral density at the Fermi level. We find that at strong lattice potentials sectors of the Fermi surface are unexpectedly destroyed and the Fermi surface becomes an arc-like disconnected manifold. We explain this phenomenon in terms of a collision of the Fermi surface pole with ze…
In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein-Maxwell-Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases…
We construct a two-current model. It includes two gauge fields, which introduce the doping effect, and a neutral scalar field. And then we numerically construct an AdS black brane geometry with scalar hair. Over this background, we study the fermionic system with the pseudoscalar Yukawa coupling. Some universal properties from the pseudoscalar Yukawa coupling are revealed. In particular, as the coupling increases, there is a transfer of the spectral weight from the low energy band to the high energy band. The transfer is over low energy scales but not over all energy scales. The peculiar prope…
We classify the different phases by the "pole-zero mechanism" for a holographic fermionic system which contains a dipole coupling with strength $p$ on a Q-lattice background. A complete phase structure in $p$ space can be depicted in terms of Fermi liquid, non-Fermi liquid, Mott phase and pseudo-gap phase. In particular, we find that in general the region of the pseudo-gap phase in $p$ space is suppressed when the Q-lattice background is dual to a deep insulating phase, while for an anisotropic background, we have an anisotropic region for the pseudo-gap phase in $p$ space as well. In addition…
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 …
We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is effectively four-dimensional and has proved surprisingly successful in recovering qualitative and quantitative properties of QCD. We investigate fluctuations of the fermionic fields on the probe D8-brane and interpret these as mesinos (fermionic superpartners of mesons). We demonstrate that the masses of these modes are comparable to meson masses and show that their i…
We study the fermionic spectral function in a holographic superconductor model. At zero temperature, the black hole has zero horizon and hence the entropy of the system is zero after the back reaction of the condensate is taken into account. We find the system exhibits the famous peak-dip-hump lineshape with a sharp low-energy peak followed by a dip then a hump at higher energies. This feature is widely observed in the spectrum of several high-T_c superconductors. We also find a linear relation between the gap in the fermionic spectrum and the condensate, indicating the condensate is formed by…
We have studied holographic Wilsonian renormalization group (HWRG) of free massless fermionic fields in AdS space and its stochastic quantization(SQ) by identifying the Euclidean action with its boundary on-shell action. The natural extension of the relation between stochastic 2-point correlation function and double trace coupling obtained from HWRG computation conjectured in arXiv:1209.2242 to fermionic fields is established. We have confirmed that the stochastic 2-point function precisely captures the radial flow of the double trace coupling via this relation.
We construct a holographic model for a fermionic system on Q-lattice and compute the spectral function in the presence of a dipole coupling. Both key features of doped Mott insulators, the dynamical generation of a gap and spectral weight transfer, are observed when adjusting the value of the coupling parameter $p$. Of particular interest is that when the background is in a deep insulating phase, the Mott gap opens much easier with a smaller coupling parameter in comparison with a metallic background. The effects of lattice parameters on the width of the gap $Δ/μ$ are studied and a turning poi…
We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-…
We construct a semiholographic effective theory in which the electron of a two-dimensional band hybridizes with a fermionic operator of a critical holographic sector, while also interacting with other bands that preserve quasiparticle characteristics. Besides the scaling dimension $ν$ of the fermionic operator in the holographic sector, the effective theory has two {dimensionless} couplings $α$ and $γ$ determining the holographic and Fermi-liquid-type contributions to the self-energy respectively. We find that irrespective of the choice of the holographic critical sector, there exists a ratio …
We use gauge-gravity duality to compute spectral functions of fermionic operators in a strongly-coupled defect field theory in p-wave superfluid states. The field theory is (3+1)-dimensional N=4 supersymmetric SU(Nc) Yang-Mills theory, in the 't Hooft limit and with large coupling, coupled to two massless flavors of (2+1)-dimensional N=4 supersymmetric matter. We show that a sufficiently large chemical potential for a U(1) subgroup of the global SU(2) isospin symmetry triggers a phase transition to a p-wave superfluid state, and in that state we compute spectral functions for the fermionic sup…
We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like di…
We study holographic Wilsonian renormalization group flows for bulk spinor fields in AdS. We use this to compute the all-loop beta function for fermionic double trace operators in the dual conformal field theory.
Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme developed in a companion work (Ref.[1]) to the study of two archetypal models of stongly correlated lattice electrons, one with translation invariance and one without. We obtain detailed insight into the emergence of various gapless and gapped phases of quantum electronic matter by computing effective Hamiltonians as well as entanglement signatures through their r…
We study a holographic toy model by considering a probe fermion of finite charge density in an anisotropic background. By computing the fermionic spectral function numerically, we observed that the system exhibits some interesting behaviours in the nature of the Fermi surface (FS) and its evolution when tuning the controlling parameters. We introduced non-minimal interaction terms in the action for holographic fermions along with a complex scalar field but neglecting the backreaction of the fermions field on the background. Suppression in the spectral weight and deformation of FS is observed, …
We study fermions in a domain wall backgrounds in five dimensional supergravity, which is similar to zero temperature limit of holographic superconductor. We find the fermionic operators for small charges in the dual four dimensional theory have gapped spectrum.
The density response of charged liquids contains a collective excitation known as the plasmon. In holographic systems with translational invariance the origin of this collective excitation is traced back to the presence of zero-sound. Using a holographic model in which translational symmetry is broken pseudo-spontaneously, we show the density response is not dominated by a single isolated mode at low momentum and temperature. As a consequence, the density response contains a broad asymmetric peak with an attenuation which does not increase monotonically with momentum and temperature.
We use holography to study the ground state of a system with interacting bosonic and fermionic degrees of freedom at finite density. The gravitational model consists of Einstein-Maxwell gravity coupled to a perfect fluid of charged fermions and to a charged scalar field which interact through a current-current interaction. When the scalar field is non-trivial, in addition to compact electron stars, the screening of the fermion electric charge by the scalar condensate allows the formation of solutions where the fermion fluid is made of antiparticles, as well as solutions with coexisting, separa…
Electron stars are fluids of charged fermions in Anti-de Sitter spacetime. They are candidate holographic duals for gauge theories at finite charge density and exhibit emergent Lifshitz scaling at low energies. This paper computes in detail the field theory Green's function G^R(w,k) of the gauge-invariant fermionic operators making up the star. The Green's function contains a large number of closely spaced Fermi surfaces, the volumes of which add up to the total charge density in accordance with the Luttinger count. Excitations of the Fermi surfaces are long lived for w <~ k^z. Beyond w ~ k^z …
We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter s…
We study the addition of quantum fermionic impurities to the N=6 supersymmetric Chern-Simons-matter theories in 2+1 spacetime dimensions. The impurities are introduced by means of Wilson loops in the antisymmetric representation of the gauge group. In a holographic setup, the system is represented by considering D6-branes probing the AdS_4 x CP^3 background of type IIA supergravity. We study the thermodynamic properties of the system and show how a Kondo lattice model with holographic dimers can be constructed. By computing the Kaluza-Klein fluctuation modes of the probe brane we determine the…
We study the holographic duals of bosonic and fermionic fields and compute their Quasinormal Frequencies (QNF) by exploiting that they are massive charged fields in $\mathrm{AdS_2 \times \mathcal{K}}$. In particular, we assess the stability of the scalar and fermionic operators in Myers-Perry's black holes with equal angular momenta. We compute the central charge and the Hawking-entropy and introduce extremality parameters to determine the properties of the dual CFT. Then, we briefly discuss how detection of Spin-2 fields can pave the way for more deep understanding of the holographic principl…
Employing a thermodynamic interpretation of gravity based on the holographic principle and assuming underlying particle statistics, fermionic or bosonic, for the excitations of the holographic screen leads to Modified Newtonian Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in MOND and the Fermi energy of the holographic fermionic degrees of freedom is obtained. In this formulation the physics of MOND results from the quantum-classical crossover in the fermionic specific heat. However, due to the dimensionality of the screen, the formalism is general and applies t…
We develop a method to detect instabilities leading to nematic phases in strongly coupled metallic systems. We do so by adapting the well-known Pomeranchuk technique to a weakly coupled system of fermions in a curved asymptotically AdS bulk. The resulting unstable modes are interpreted as corresponding to instabilities on the dual strongly coupled holographic metal. We apply our technique to a relativistic $3+1$-dimensional bulk with generic quartic fermionic couplings, and explore the phase diagram at zero temperature for finite values of the fermion mass and chemical potential, varying the c…
We investigate the holographic fermionic phase transition induced by the effective impurity in holography, which is introduced by massless scalar fields in Einstein-Maxwell-massless scalar gravity. We obtain a phase diagram in $(α, T)$ plane separating the Fermi liquid phase and the non-Fermi liquid phase.
We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological $Θ$-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This r…
We study the holographic dual of a finite density system with both bosonic and fermionic degrees of freedom. There is no evidence for a universal bose-dominated ground state. Instead, depending on the relative conformal weights the preferred groundstate is either pure AdS-Reissner-Nordstrom, a holographic superconductor, an electron star, or a novel mixed state that is best characterized as a hairy electron star.
We study the effects of a non-zero magnetic field on a class of 2+1 dim non-Fermi liquids, recently found in 0903.2477 by considering properties of a fermionic probe in an extremal AdS^4 black hole background. Introducing a similar fermionic probe in a dyonic AdS^4 black hole geometry, we find that the effect of a magnetic field could be incorporated in a rescaling of the probe fermion's charge. From this simple fact, we observe interesting effects like gradual disappearance of the Fermi surface and quasi particle peaks at large magnetic fields and changes in other properties of the system. We…
The holographic principle in the pp-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super Yang-Mills theory holds to the leading order in the large $μ$ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds …
We study cold fermionic atoms using the holographic principle. We note that current atomic experiments with massive fermions trapped in a harmonic potential in the unitarity limit behave as massless fermions thanks to the Thomas-Fermi approximation. We map the thermodynamics of strongly correlated massless fermion to that of the charged black hole and study the thermodynamics and transport properties of cold fermions at strong coupling at finite temperature and density. In cold limit, the specific heat of charged black hole is linear in $T$ independent of the dimensionality, which is reminisce…
We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $\barψγ^{μν}ψ$ and $\barψγ^{μν}γ^5ψ$. We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spec…
Robustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating theta-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robus…
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points are close to the real axis, the system typically exhibits walking behavior with Miransky (or Berezinsky-Kosterlitz-Thouless) scaling. We present a novel realization of these phenomena at strong coupling by means of the gauge/gravity duality, and give evidence for the conjectured existence of complex conformal field theories at the fixed points.
Motivated by the holographic complexity proposals, in this paper, we investigate the time dependence of the complexity for the Fermionic thermofield double state (TFD) using the Nielsen approach and Fubini-Study (FS) approach separately. In both two approaches, we discuss the results for different reference states: the Dirac vacuum state and the Gaussian state which has no spatial entanglement (NSE). For Dirac vacuum reference state, we find that the complexity by both two approaches is time independent and the circuit complexity shares the same expression for both methods with the $L^2$ norm.…
Entanglement entropy is a useful probe of compressible quantum matter because it can detect the existence of Fermi surfaces, both of microscopic fermionic degrees of freedom and of "hidden" gauge charged fermions. Much recent attention has focused on holographic efforts to model strongly interacting compressible matter of interest for condensed matter physics. We complete the entanglement analysis initiated in Huijse {\em et al.}, Phys. Rev. B 85, 035121 (2012) (arXiv:1112.0573) and Ogawa {\em et al.}, JHEP 1, 125 (2012) (arXiv:1111.1023) using the recent proposal of Faulkner {\em et al.} (arX…
We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2)^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2)^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFT's. In the bosonic QED's the merging happens around $N_f\sim 9{-}11$ and does not break the global symmetry. In the fermionic QED's the merging happens around $N_f\sim3{-}…
We consider the gravity dual of strongly coupled system at a Lifshitz-fixed point and finite temperature, which was constructed in a recent work arXiv:0909.0263. We construct an Abelian Higgs model in that background and calculate condensation and conductivity using holographic techniques. We find that condensation happens and DC conductivity blows up when temperature turns below a critical value.
