Holographic low-energy spectral weight at zero temperature and finite momenta indicates the presence of a strongly coupled remnant of Pauli exclusion. Building upon previous work, we study the spectral weight of a bottom-up holographic superfluid model with spontaneously broken translational symmetry. We determine the effect of this symmetry breaking on the previously known attributes of the holographic superconductor spectral weight: 1) an instability at finite momenta and 2) the presence of nested Fermi surfaces (sometimes called Fermi shells). We find that the symmetry breaking seems to strengthen the former and suppress the latter, in a way that we describe.
We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results.
We study the electrical response of a wide class of strange metal phases without quasiparticles at finite temperature and charge density, with explicitly broken translational symmetry, using holography. The low frequency electrical conductivity exhibits a Drude peak, so long as momentum relaxation is slow. The relaxation time and the direct current conductivity are exactly equal to what is computed, independently of holography, via the memory function framework.
We compute anomalous transport phenomena sourced by vector and axial magnetic fields in out of equilibrium setups produced by Vaidya background metrics in holography. We use generalized Vaidya metrics that include momentum relaxation induced by massless scalar fields. While the background metric and gauge field show formally instantaneous thermalization the chiral magnetic effect has significantly large equilibration times. We study how the equilibration of the chiral magnetic effect depends on the length of the Vaidya quench and the momentum relaxation parameter. These results shed some light…
We expand the holographic studies of momentum relaxation to include non-relativistic scaling symmetries in the ultraviolet. We do so by constructing black branes with Lifshitz asymptotics dressed with axions which explicitly depend on the boundary directions. Such configurations arise as analytic solutions of the Einstein-Proca theory coupled to massless scalar fields in arbitrary dimensions. Studying linear perturbations on these backgrounds, we conclude that there is a dual Ward identity which accounts for the dissipation of momentum in the system. In addition, we numerically compute the fre…
We study the mechanical response under time-dependent sources of a simple class of holographic models that exhibit viscoelastic features. The ratio of viscosity over elastic modulus defines an intrinsic relaxation time scale -- the so-called Maxwell relaxation time $τ_M$, which has been identified traditionally with the relaxation time scale. We compute explicitly the relaxation time in our examples and that it differs from $τ_M$. At high temperatures $τ_M$ over-estimates the actual relaxation time, although not by much and moreover it still captures reasonably well the temperature behaviour. …
We provide a complete and unified description of translational symmetry breaking in a simple holographic model. In particular, we focus on the distinction and the interplay between explicit and spontaneous breaking. We consider a class of holographic massive gravity models which allow to range continuously from one situation to the other. We study the collective degrees of freedom, the electric AC conductivity and the shear correlator in function of the explicit and spontaneous scales. We show the possibility of having a sound-to-diffusion crossover for the transverse phonons. Within our model…
We study the magnetoconductivity induced by the axial anomaly via the chiral magnetic effect in strongly coupled holographic models. An important ingredient in our models is that the axial charge is non-conserved beyond the axial anomaly. We achieve this either by explicit symmetry breaking via a non-vanishing non-normalisable mode of an axially charged scalar or using a Stuckelberg field to make the AdS-bulk gauge field massive. The DC magnetoconductivites can be calculated analytically. They take a universal form in terms of gauge field mass at the horizon and quadratic dependence on the mag…
We study the viscosity spectral function of a holographic 2+1 dimensional fluid with Schroedinger symmetry. The model is based on a twisted compactification of $Ads_5\times S_5$. We numerically compute the spectral function of the stress tensor correlator for all frequencies, and analytically study the limits of high and low frequency. We compute the shear viscosity, the viscous relaxation time, and the quasi-normal mode spectrum in the shear channel. We find a number of unexpected results: The high frequency behavior is governed by a fractional 1/3 power law, the viscous relaxation time is ne…
We investigate the Drude weight and the related Mazur-Suzuki (MS) bound in a broad variety of strongly coupled field theories with a gravity dual at finite temperature and chemical potential. We revisit the derivation of the recently proposed universal expression for the Drude weight for Einstein-Maxwell-dilaton (EMd) theories and extend it to the case of theories with multiple massless gauge fields. We show that the MS bound, which in the context of condensed matter provides information on the integrability of the theory, is saturated in these holographic theories including R-charged backgrou…
We provide a comprehensive classification of isotropic solid and fluid holographic models with broken translational invariance. We describe in detail the collective modes in both the transverse and longitudinal sectors. First, we discuss holographic fluid models, i.e. systems invariant under internal volume preserving diffeomorphisms. We consider the explicit (EXB) and the spontaneous (SSB) breaking of translations and we emphasize the differences with respect to their solid counterpart. Then, we present a study of the longitudinal collective modes in simple holographic solid and fluid models …
We investigate the low-energy dynamics of systems with pseudo-spontaneously broken $U(1)$ symmetry and Goldstone phase relaxation. We construct a hydrodynamic framework which is able to capture these, in principle independent, effects. We consider two generalisations of the standard holographic superfluid model by adding an explicit breaking of the $U(1)$ symmetry by either sourcing the charged bulk scalar or by introducing an explicit mass term for the bulk gauge field. We find agreement between the hydrodynamic dispersion relations and the quasi-normal modes of both holographic models. We ve…
Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature d.c. resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface structure, leading to the well-known relaxation rate Gamma ~ T^2. We observe that local criticality, in which energies scale but momenta do not, provides a distinct route to efficient umklapp scattering. We show that umklapp scattering by an ionic lattice in a locally critical theory leads to Gamma ~ T^(2Δ(k_L)). Here Δ(k_L) \geq 0 is the dimension of the (irrelevant…
We study the chiral vortical effect far from equilibrium in a strongly coupled holographic field theory. Rotation is represented as a perturbation via a gravito-magnetic field on top of a five-dimensional charged AdS Vaidya metric. We also introduce a momentum relaxation mechanism by linear scalar field backgrounds and study the CVE dynamics as function of the charges, temperature and momentum relaxation. The far from equilibrium behavior shows that the CVE builds up with a significant delay in time compared to the quasi instantaneous equilibration of the background metric. We also pay special…
We study the holographic dual of a (2+1)-dimensional s-wave superfluid that breaks an abelian U(1) x U(1) global symmetry group to the diagonal U(1)_V. The model is inspired by Sen's tachyonic action, and the operator that condenses transforms in the bifundamental representation of the symmetry group. We focus on two configurations: the first one describes a marginal operator, and the phase diagram at finite temperature contains a first or a second order phase transition, depending on the parameters that determine the theory. In the second model the operator is relevant and the finite temperat…
We study the effects of momentum relaxation on the holographic Weyl semimetal which exhibits a topological quantum phase transition between the Weyl semimetal phase and a topological trivial phase. The conservation of momentum in the field theory is broken by the axion fields in holography. The topological Weyl semimetal phase is characterized by a nontrivial anomalous Hall conductivity. We find that the critical value of the phase transition decreases when we increase the momentum relaxation strength up to a special value, above which it goes to zero. This indicates that the Weyl semimetal ph…
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.
Using holography, we model experiments in which a 2+1D strange metal is pumped by a laser pulse into a highly excited state, after which the time evolution of the optical conductivity is probed. We consider a finite-density state with mildly broken translation invariance and excite it by oscillating electric field pulses. At zero density, the optical conductivity would assume its thermalized value immediately after the pumping has ended. At finite density, pulses with significant DC components give rise to slow exponential relaxation, governed by a vector quasinormal mode. In contrast, for hig…
Momentum relaxation is an ever-present and unavoidable ingredient of any realistic condensed matter system. In real-world materials the presence of a lattice, impurities or disorder forces momentum to dissipate and leads to relevant physical effects such as the finiteness of the DC transport properties, i.e. conductivities. The main purpose of this thesis is the introduction of momentum dissipation and its consequent effects into the framework of AdS/CMT, namely the applications of the gauge-gravity duality to condensed matter. A convenient and effective way of breaking the translational symme…
In the fermionic sector of top-down approaches to holographic systems, one generically finds that the fermions are coupled to gravity and gauge fields in a variety of ways, beyond minimal coupling. In this paper, we take one such interaction -- a Pauli, or dipole, interaction -- and study its effects on fermion correlators. We find that this interaction modifies the fermion spectral density in a remarkable way. As we change the strength of the interaction, we find that spectral weight is transferred between bands, and beyond a critical value, a hard gap emerges in the fermion density of states…
We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as governed by the vector quasi-normal modes of the dual black brane, whose spectrum depends qualitatively on a parameter controlling the strength of inhomogeneity. We explore the dynamical phase diagram as a function of this parameter, showing that signatures of incoherent transport become identifiable as an oscillatory ringdown of the heat current. We also study non…
We propose the holographic description of the Lifshitz tail typical for one-particle spectral density of bounded disordered system in $D=1$ space. To this aim the "polymer representation" of the Jackiw-Teitelboim (JT) 2D dilaton gravity at a finite cutoff is used and the corresponding partition function is considered as the weighted sum over paths of fixed length in an external magnetic field. We identify the regime of small loops, responsible for emergence of a Lifshitz tail in the Gaussian disorder, and relate the strength of disorder to the boundary value of the dilaton. The geometry corres…
Hydrodynamics is a theory of long-range excitations controlled by equations of motion that encode the conservation of a set of currents (energy, momentum, charge, etc.) associated with explicitly realized global symmetries. If a system possesses additional weakly broken symmetries, the low-energy hydrodynamic degrees of freedom also couple to a few other "approximately conserved" quantities with parametrically long relaxation times. It is often useful to consider such approximately conserved operators and corresponding new massive modes within the low-energy effective theory, which we refer to…
The Pomeranchuk instability, in which an isotropic Fermi surface distorts and becomes anisotropic due to strong interactions, is a possible mechanism for the growing number of experimental systems which display transport properties that differ along the $x$ and $y$ axes. We show here that the gauge-gravity duality can be used to describe such an instability in fermionic systems. Our holographic model consists of fermions in a background which describes the causal propagation of a massive neutral spin-two field in an asymptotically AdS spacetime. The Fermi surfaces in the boundary theory distor…
In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizin…
