arXiv subjects

Matteo Baggioli

Publications and source records attributed to Matteo Baggioli.

At least 127 records · Page 7Linked to original sources

arXiv2020

Universal Bounds on Transport in Holographic Systems with Broken Translations

We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We verify numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be violated but the shear diffusion constant remains bounded by below. This confirms the idea that $η/s$ loses its privileged role in non-relativistic systems and that, in order to find more universal bounds, one should rather look at diffusion constants. We strengthen this idea by showing that, in presence of spontaneously broken translations, the Goldstone diffusion constant satisfies a universal lower bound in terms of the Planckian relaxation time and the butterfly velocity. Additionally, all the diffusive processes in the model satisfy an upper bound, imposed by causality, which is given in terms of the thermalization time -- the imaginary part of the first non-hydrodynamic mode in the spectrum -- and the speed of longitudinal sound. Finally, we discuss the existence of a bound on the speed of sound in holographic conformal solids and we show that the conformal value acts as a lower (and not upper) bound on the speed of longitudinal phonons. Nevertheless, we show that the stiffness $\partial p/\partial ε$ is still bounded by above by its conformal value. This suggests that the bounds conjectured in the past have to be considered on the stiffness of the system, related to its equation of state, and not on the propagation speed of sound.

hep-th↗

arXiv2020

Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids

We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds - the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress-strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress-strain curves - with two different power-law regimes at different magnitudes of the strain.

hep-th↗

arXiv2020

Elasticity bounds from Effective Field Theory

Phonons in solid materials can be understood as the Goldstone bosons of the spontaneously broken spacetime symmetries. As such their low energy dynamics are greatly constrained and can be captured by standard effective field theory (EFT) methods. In particular, knowledge of the nonlinear stress-strain curves completely fixes the full effective Lagrangian at leading order in derivatives. We attempt to illustrate the potential of effective methods focusing on the so-called hyperelastic materials, which allow large elastic deformations. We find that the self-consistency of the EFT imposes a number of bounds on physical quantities, mainly on the maximum strain and maximum stress that can be supported by the medium. In particular, for stress-strain relations that at large deformations are characterized by a power-law behaviour $σ(\varepsilon)\sim \varepsilon^ν$, the maximum strain exhibits a sharp correlation with the exponent $ν$.

hep-th↗

arXiv2020

Effective Theory of Superconductivity in Strongly-Coupled Amorphous Materials

A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusive-like transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $α^{2}F(ω)$ in comparison with experiments, and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on one hand drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $ω_{log}$ in the Allen-Dynes formula. As a consequence, the non-monotonicity of $T_{c}$ as a function of alloying (disorder) in $\text{Pb}$-based systems can be rationalized. The case of $\text{Al}$-based systems, where disorder increases $T_{c}$ from the start, is also analyzed. General material-design principles for enhancing $T_{c}$ in amorphous superconductors are presented.

cond-mat.supr-con↗

arXiv2020

Magnetophonons & type-B Goldstones from Hydrodynamics to Holography

We perform a detailed analysis of a large class of effective holographic models with broken translations at finite charge density and magnetic field. We exhaustively discuss the dispersion relations of the hydrodynamic modes at zero magnetic field and successfully match them to the predictions from charged hydrodynamics. At finite magnetic field, we identify the presence of an expected type-B Goldstone boson $\mathrm{Re}[ω]\sim k^2$, known as magnetophonon and its gapped partner -- the magnetoplasmon. We discuss their properties in relation to the effective field theory and hydrodynamics expectations. Finally, we compute the optical conductivities and the quasinormal modes at finite magnetic field. We observe that the pinning frequency of the magneto-resonance peak increases with the magnetic field, in agreement with experimental data on certain 2D materials, revealing the quantum nature of the holographic pinning mechanism.

hep-th↗

arXiv2020

Physics of Phonon-Polaritons in Amorphous Materials

The nature of bosonic excitations in disordered materials has remained elusive due to the difficulties in defining key concepts such as quasi-particles in the presence of disorder. We report on the experimental observation of phonon-polaritons in glasses, including a boson peak (BP), i.e. excess of THz modes over the Debye law. A theoretical framework based on the concept of diffusons is developed to model the broadening linewidth of the polariton due to disorder-induced scattering. It is shown that the scaling of the BP frequency with the diffusion constant of the linewidth strongly correlates with that of the Ioffe-Regel (IR) crossover frequency of the polariton. This result demonstrates the universality of the BP in the low-energy spectra of collective bosonic-like excitations in glasses, well beyond the traditional case of acoustic phonons, and establishes the IR crossover as the fundamental physical mechanism behind the BP.

cond-mat.dis-nn↗

arXiv2020

Homogeneous Holographic Viscoelastic Models & Quasicrystals

We show that the field theories dual to the homogeneous holographic models with spontaneously broken translations display several distinctive properties of quasicrystals, aperiodic crystals with long-range order (e.g. incommensurate charge density waves). This interpretation suggests that the longitudinal diffusive mode, observed in the spectrum of excitations of these systems, is the diffusive Goldstone boson typical of quasicrystals -- the phason. Moreover, following this idea, and using the effective field theory formalism for Goldstone modes in dissipative systems, we are able to derive the universal phase relaxation found in these holographic models in presence of a small source of explicit breaking (pseudo-spontaneous regime).

hep-th↗

arXiv2020

Gapped momentum states

Important properties of a particle, wave or a statistical system depend on the form of a dispersion relation (DR). Two commonly-discussed dispersion relations are the gapless phonon-like DR and the DR with the energy or frequency gap. More recently, the third and intriguing type of DR has been emerging in different areas of physics: the DR with the gap in momentum, or $k$-space. It has been increasingly appreciated that gapped momentum states (GMS) have important implications for dynamical and thermodynamic properties of the system. Here, we review the origin of this phenomenon in a range of physical systems, starting from ordinary liquids to holographic models. We observe how GMS emerge in the Maxwell-Frenkel approach to liquid viscoelasticity, relate the $k$-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space and vice versa. We subsequently discuss how GMS emerge in the two-field description which is analogous to the quantum formulation of dissipation in the Keldysh-Schwinger approach. We discuss experimental evidence for GMS, including the direct evidence of gapped DR coming from strongly-coupled plasma. We also discuss GMS in electromagnetic waves and non-linear Sine-Gordon model. We then move on to discuss the recently developed quasihydrodynamic framework which relates the $k$-gap with the presence of a softly broken global symmetry and its applications. Finally, we review recent discussions of GMS in relativistic hydrodynamics and holographic models. Throughout the review, we point out essential physical ingredients required by GMS to emerge and make links between different areas of physics, with the view that new and deeper understanding will benefit from studying the GMS in seemingly disparate fields and from clarifying the origin of potentially similar underlying physical ideas and equations.

cond-mat.stat-mech↗

arXiv2020

Transverse Collective Modes in Interacting Holographic Plasmas

We study in detail the transverse collective modes of simple holographic models in presence of electromagnetic Coulomb interactions. We render the Maxwell gauge field dynamical via mixed boundary conditions, corresponding to a double trace deformation in the boundary field theory. We consider three different situations: (i) a holographic plasma with conserved momentum, (ii) a holographic (dirty) plasma with finite momentum relaxation and (iii) a holographic viscoelastic plasma with propagating transverse phonons. We observe two interesting new features induced by the Coulomb interactions: a mode repulsion between the shear mode and the photon mode at finite momentum relaxation, and a propagation-to-diffusion crossover of the transverse collective modes induced by the finite electromagnetic interactions. Finally, at large charge density, our results are in agreement with the transverse collective mode spectrum of a charged Fermi liquid for strong interaction between quasi-particles, but with an important difference: the gapped photon mode is damped even at zero momentum. This property, usually referred to as anomalous attenuation, is produced by the interaction with a quantum critical continuum of states and might be experimentally observable in strongly correlated materials close to quantum criticality, e.g. in strange metals.

hep-th↗

arXiv2020

Scale invariant solids

Scale invariance (SI) can in principle be realized in the elastic response of solid materials. There are two basic options: that SI is a manifest symmetry or that it is spontaneously broken. The manifest case corresponds physically to the existence of a non-trivial infrared fixed point with phonons among its degrees of freedom. We use simple bottom-up AdS/CFT constructions to model this case. We characterize the types of possible elastic response and discuss how the sound speeds can be realistic, that is, sufficiently small compared to the speed of light. We also study the spontaneously broken case using Effective Field Theory (EFT) methods. We present a new one-parameter family of nontrivial EFTs that includes the previously known `conformal solid' as a particular case as well as others which display small sound speeds. We also point out that an emergent Lorentz invariance at low energies could affect by order-one factors the relation between sound speeds and elastic moduli.

hep-th↗

arXiv2020

Theory of the phonon spectrum in host-guest crystalline solids with avoided crossing

We develop an analytical model to describe the phonon dispersion relations of host-guest lattices with heavy guest atoms (rattlers). Crucially, the model also accounts for phonon damping arising from anharmonicity. The spectrum of low energy states contains acoustic-like and (soft) optical-like modes, which display the typical avoided crossing, and which can be derived analytically by considering the dynamical coupling between host lattice and guest rattlers. Inclusion of viscous anharmonic damping in the model allows us, for the first time, to compute the vibrational density of states (VDOS) and the specific heat, unveiling the presence of a boson peak (BP) linked to an anharmonicity-smeared van Hove singularity. Upon increasing the coupling strength between the host and the guest dynamics, and by decreasing the energy of the soft optical modes, the BP anomaly becomes stronger and it moves towards lower frequencies. Moreover, we find a robust linear correlation between the BP frequency and the energy of the soft optical-like modes. This framework provides a useful model for tuning the thermal properties of host-guest lattices by controlling the VDOS, which is crucial for optimizing thermal conductivity and hence the energy conversion efficiency in these materials.

cond-mat.mtrl-sci↗

arXiv2020

Nonlinear Oscillatory Shear Tests in Viscoelastic Holography

We provide the first characterization of the nonlinear and time dependent rheologic response of viscoelastic bottom-up holographic models. More precisely, we perform oscillatory shear tests in holographic massive gravity theories with finite elastic response, focusing on the large amplitude oscillatory shear (LAOS) regime. The characterization of these systems is done using several techniques: (I) the Lissajous figures, (II) the Fourier analysis of the stress signal, (III) the Pipkin diagram and (IV) the dependence of the storage and loss moduli on the amplitude of the applied strain. We find substantial evidence for a strong strain stiffening mechanism, typical of hyper-elastic materials such as rubbers and complex polymers. This indicates that the holographic models considered are not a good description for rigid metals, where strain stiffening is not commonly observed. Additionally, a crossover between a viscoelastic liquid regime at small graviton mass (compared to the temperature scale), and a viscoelastic solid regime at large values is observed. Finally, we discuss the relevance of our results for soft matter and for the understanding of the widely used homogeneous holographic models with broken translations.

hep-th↗

arXiv2019

A Practical Mini-Course on Applied Holography

This is a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019. It is supposed to be a concise (and therefore not comprehensive) and pragmatic course on applied holography and especially the (basic) analytic and numerical techniques involved. The lectures are not focused on the large theoretical and fundamental background which can be found already in several places in the literature, but rather on concrete applications of Bottom-Up AdS-CFT to Hydrodynamics, QCD and Condensed Matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details of the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during my research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by himself/herself more advanced techniques and to produce independent and novel research on the topic.

hep-th↗

arXiv2019

Viscoelastic Dynamics in Holography

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. At sufficiently low temperatures the situation is reversed: $τ_M$ underestimates the actual relaxation time, in some cases quite drastically. Moreover, when $τ_M$ under-estimates the real-time response exhibits an overshoot phenomenon before relaxation. We comment on the $T = 0$ limit, where the relaxation is power-law because our models exhibit criticality.

hep-th↗

arXiv2019

Unified theory of vibrational spectra in amorphous materials

The phonon spectra of solids, described through the measurable vibrational density of states (VDOS), provide a wealth of information about the underlying atomic structure and bonding, and they determine fundamental macroscopic properties such as specific heat, thermal conductivity and superconductivity. In amorphous solids, structural disorder generates a number of poorly understood phenomena that are absent in crystals. Starting from an effective field theory description which accounts for disorder in terms of momentum diffusion, we provide a unified theoretical description of the VDOS of amorphous materials. The theory provides an excellent description of the simulated/experimental VDOS of two quite different materials (silica glass and amorphous Si) with very few non-trivial fitting parameters. In particular, the phonons speeds and diffusive linewidths obtained from the fits are fully consistent with the tabulated values from experiments. This semi-analytical approach solves the long-standing problem of describing and explaining the features of the VDOS and Raman spectra of amorphous solids in relation with the underlying acoustic dispersion relations and acoustic attenuation. Furthermore, it can be used in a reverse-engineered way to estimate phonon dispersion relations, acoustic attenuation and dynamic structure factors from a simple fitting of the VDOS with the presented model.

cond-mat.mtrl-sci↗

arXiv2019

Zoology of Solid & Fluid Holography : Goldstone Modes and Phase Relaxation

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 exhibiting the interplay between SSB and EXB. We confirm the presence of light pseudo-phonons obeying the Gell-Mann-Oakes-Renner relation and the validity of the relation proposed in the literature between the novel phase relaxation scale, the mass of the pseudo-Golstone modes and the Goldstone diffusion. Moreover, we find very good agreement between the dispersion relation of our longitudinal sound mode and the formulae derived from the Hydro$+$ framework. Finally, our results suggest that the crystal diffusion mode does not acquire a simple damping term because of the novel relaxation scale proportional to the EXB. The dynamics is more complex and it involves the interplay of three modes: the crystal diffusion and two more arising from the splitting of the original sound mode. In this sense, the novel relaxation scale, which comes from the explicit breaking of the global internal shift symmetry of the Stückelberg fields, is different from the one induced by elastic defects, and depending solely on the SSB scale.

hep-th↗

arXiv2019

Holographic Plasmon Relaxation with and without Broken Translations

We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.

hep-th↗

arXiv2019

Hydrodynamics of disordered marginally-stable matter

We study the vibrational spectra and the specific heat of disordered systems using an effective hydrodynamic framework. We consider the contribution of diffusive modes, i.e. the 'diffusons', to the density of states and the specific heat. We prove analytically that these new modes provide a constant term to the vibrational density of states $g(ω)$. This contribution is dominant at low frequencies, with respect to the Debye propagating modes. We compare our results with numerical simulations data and random matrix theory. Finally, we compute the specific heat and we show the existence of a linear in $T$ scaling $C(T) \sim c\,T$ at low temperatures due to the diffusive modes. We analytically derive the coefficient $c$ in terms of the diffusion constant $D$ of the quasi-localized modes and we obtain perfect agreement with numerical data. The linear in $T$ behavior in the specific heat is stronger the more localized the modes, and crosses over to a $T^{3}$ (Debye) regime at a temperature $T^{*}\sim \sqrt{v^{3}/D}$, where $v$ is the speed of sound. Our results suggest that the anomalous properties of glasses and disordered systems can be understood effectively within a hydrodynamic approach which accounts for diffusive quasi-localized modes generated via disorder-induced scattering.

cond-mat.dis-nn↗