arXiv subjects

Blaise Goutéraux

Publications and source records attributed to Blaise Goutéraux.

At least 19 recordsLinked to original sources

arXiv2026

Schwarzian quantum corrections to shear correlators of the near-extremal Reissner-Nordström-AdS black hole

Near-AdS$_2$ spacetimes are controlled by a Schwarzian effective dual theory. The Kaluza-Klein reduction of higher-dimensional black holes shows that the Schwarzian generates a logarithmic contribution to the entropy, thereby resolving a long-standing puzzle in near-extremal black hole thermodynamics. Here, we leverage exact results for quantum-corrected, Schwarzian scalar correlation functions in order to evaluate the impact of bulk quantum fluctuations on the low-temperature shear correlators of the state dual to Reissner-Nordström-AdS$_4$ black holes with a flat, compact horizon. In the hydrodynamic regime, we find that quantum fluctuations tend to increase the shear viscosity away from $s/(4π)$, thereby preserving the Kovtun-Son-Starinets bound. Outside the hydrodynamic regime, quantum fluctuations lift the zero temperature, classical gapless modes reported in previous literature.

hep-th↗

arXiv2026

Electronic Sound and Diffusion in Disordered Multiband Metals

Multiband metals can host acoustic plasmons: gapless collective charge excitations involving out-of-phase motion of electrons in different bands, sometimes referred to as 'demons'. Using a hydrodynamic description valid at high temperatures, and a microscopic description with vertex corrections valid at low temperatures, we show, upon including disorder inevitably present in real materials, that the mode frequency becomes purely imaginary, resulting in diffusive behaviour over a finite range of small wave vectors $q\le q_c$. This framework provides a natural, parameter-free explanation for the anomalous nonlinear dispersion recently reported for the demon in Sr$_2$RuO$_4$, which deviates from the gapless behaviour predicted by the random phase approximation. Our results establish demons as fundamentally distinct from previously known acoustic excitations, such as phonons and photons, which exhibit inertial dynamics protected by symmetries or gauge redundancies.

cond-mat.str-el↗

arXiv2026

Counterflow and coflow instabilities in miscible binary superfluids

We explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis, which applies to interacting many-body systems at finite temperature. We find that the onset of these instabilities is signaled by the determinant of the Hessian of the thermal free energy diverging and changing sign. We verify this hydrodynamic prediction in a holographic binary superfluid modeled with gauge/gravity duality, which naturally incorporates strong coupling, finite temperature, and dissipation. We also compare to results obtained using the Gross-Pitaevskii equation for weakly interacting Bose-Einstein condensates and find that the same criterion continues to apply at zero temperature, where it reduces to evaluating derivatives of the supercurrents with respect to the superfluid velocities. We observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. Finally, the nonlinear stages of the instabilities are studied by full time evolution using gauge/gravity duality, where vortex annihilation leads to a decrease of superfluid velocity back to a value where the binary superfluid phase is stable.

hep-th↗

arXiv2025

Near-extremal holographic charge correlators

We analytically compute the low-temperature charge correlators in near-extremal black holes with a planar horizon and an infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ extremal geometry, finding excellent agreement with numerical calculations. The analytical result consistently describes the crossover between the hydrodynamic diffusive regime at low frequencies and wavenumbers, and the quantum, zero-temperature regime at high frequencies and wavenumbers. We analytically resolve the successive collisions between the diffusive pole and the non-hydrodynamic poles sourced by the infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ geometry. We demonstrate that in the $T=0$ limit, a pair of gapless poles survive with a dispersion relation $ω_\pm=-i d_2 k^2-i d_4 k^4-i\tilde d_4 k^4(\pm iπ+\log k^2) $. The nonanalytic contributions arise from the interplay with the branch cut formed by the condensation of the non-hydrodynamic poles. The real part is caused by the `snatching' of one of the non-hydrodynamic poles by the hydrodynamic diffusive pole.

hep-th↗

arXiv2024

Linear dynamical stability and the laws of thermodynamics

We show that the dynamical stability under linear perturbations of interacting systems in the hydrodynamic regime follows from the first and the second laws of thermodynamics. Our argument extends to systems with spontaneously or softly broken symmetries and in the presence of magnetic fields.

hep-th↗

arXiv2024

Beyond Drude transport in hydrodynamic metals

In interacting theories, hydrodynamics describes the universal behavior of states close to local thermal equilibrium at late times and long distances in a gradient expansion. In the hydrodynamic regime of metals, momentum relaxes slowly with a rate $Γ$, which formally appears on the right-hand side of the momentum dynamical equation and causes a Drude-like peak in the frequency dependence of the thermoelectric conductivities. Here we study the structure and determine the physical implications of momentum-relaxing gradient corrections beyond Drude, \emph{i.e.} arising at subleading order in the gradient expansion. We find that they effectively renormalize the weight of the Drude pole in the thermoelectric conductivities, and contribute to the dc conductivities at the same order as previously-known gradient corrections of translation-invariant hydrodynamics. Turning on a magnetic field, extra derivative corrections appear and renormalize the cyclotron frequency and the Hall conductivity. This relaxed hydrodynamics provides a field-theoretic explanation for previous results obtained using gauge-gravity duality. In strongly-coupled metals where quasiparticles are short-lived and which may be close to a hydrodynamic regime, the extra contributions we discuss are essential to interpret experimentally measured magneto-thermoelectric conductivities. Specializing to metals close to a Fermi liquid phase, the effective mass measured either through the specific heat or the spectral weight of the Drude-like peak are found to differ, as was indeed reported in overdoped cuprate superconductors. More generally, we expect such terms to be present in any hydrodynamic theory with approximate symmetries, which arise in many physical systems.

hep-th↗

arXiv2023

Hydrodynamics and instabilities of relativistic superfluids at finite superflow

We study the linear response of relativistic superfluids with a non-zero superfluid velocity. For sufficiently large superflow, an instability develops via the crossing of a pole of the retarded Green's functions to the upper half complex frequency plane. We show that this is caused by a local thermodynamic instability, i.e. when an eigenvalue of the static susceptibility matrix (the second derivatives of the free energy) diverges and changes sign. The onset of the instability occurs when $\partial_ζ(n_sζ)=0$, with $ζ$ the norm of the superfluid velocity and $n_s$ the superfluid density. The Landau instability for non-relativistic superfluids such as Helium 4 also coincides with the non-relativistic version of this criterion. We then turn to gauge/gravity duality and show that this thermodynamic instability criterion applies equally well to strongly-coupled superfluids. In passing, we compute holographically a number of transport coefficients parametrizing deviations out-of-equilibrium in the hydrodynamic regime and demonstrate that the gapless quasinormal modes of the dual planar black hole match those predicted by superfluid hydrodynamics.

hep-th↗

arXiv2023

Zero sound and higher-form symmetries in compressible holographic phases

Certain holographic states of matter with a global U(1) symmetry support a sound mode at zero temperature, caused neither by spontaneous symmetry breaking of the global U(1) nor by the emergence of a Fermi surface in the infrared. In this work, we show that such a mode is also found in zero density holographic quantum critical states. We demonstrate that in these states, the appearance of a zero temperature sound mode is the consequence of a mixed `t Hooft anomaly between the global U(1) symmetry and an emergent higher-form symmetry. At non-zero temperatures, the presence of a black hole horizon weakly breaks the emergent symmetry and gaps the collective mode, giving rise to a sharp Drude-like peak in the electric conductivity. A similar gapped mode arises at low temperatures for non-zero densities when the state has an emergent Lorentz symmetry, also originating from an approximate anomalous higher-form symmetry. However, in this case the collective excitation does not survive at zero temperature where, instead, it dissolves into a branch cut due to strong backreaction from the infrared, critical degrees of freedom. We comment on the relation between our results and the application of the Luttinger theorem to compressible holographic states of matter.

hep-th↗

arXiv2022

Thermodynamic origin of the Landau instability of superfluids

In this work, we revisit the question of the linear stability of superfluid phases of matter. Famously, Landau predicted superfluid Helium would become unstable for large enough superfluid velocities. We demonstrate that this instability simply follows from a thermodynamic argument, by showing that its onset corresponds to a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Turning on dissipation and without any particular assumption on invariance under boosts, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of quasiparticles, our criterion matches Landau's critical velocity. We also verify that it correctly reproduces the onset of the instability in relativistic superfluids constructed using gauge/gravity duality. Our work provides a simple, comprehensive and unified description of the Landau instability for superfluids independently of the microscopic details of the system.

hep-th↗

arXiv2022

Colloquium: Hydrodynamics and holography of charge density wave phases

In this Colloquium, we review recent progress in the effective description of strongly-correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is inevitable and pins the Goldstones of broken translations. We describe how pinning can be incorporated in the effective field theory at low energies, without making any assumption on the presence of boost symmetry. We review the essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries. We close with a discussion on the relevance of these models for the phenomenology of dc and ac transport in strongly-correlated strange and bad metals, such as high temperature superconductors.

hep-th↗

arXiv2022

Damping of Pseudo-Goldstone Fields

Approximate symmetries abound in Nature. If these symmetries are also spontaneously broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length, and are referred to as pseudo-Goldstones. At nonzero temperature, the effects of dissipation can be captured by hydrodynamics at sufficiently long scales compared to the local equilibrium. Here we show that in the limit of weak explicit breaking, locality of hydrodynamics implies that the damping of pseudo-Goldstones is completely determined by their mass and diffusive transport coefficients. We present many applications: superfluids, QCD in the chiral limit, Wigner crystal and density wave phases in the presence of an external magnetic field or not, nematic phases and (anti-)ferromagnets. For electronic density wave phases, pseudo-Goldstone damping generates a contribution to the resistivity independent of the strength of disorder, which can have a linear temperature dependence provided the associated diffusivity saturates a bound. This is reminiscent of the phenomenology of strange metal high $T_c$ superconductors, where charge density waves are observed across the phase diagram.

hep-th↗

arXiv2021

Hydrodynamic diffusion and its breakdown near AdS$_2$ quantum critical points

Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the theory. In the vicinity of a quantum critical point, it is expected that some aspects of the dynamics are universal and dictated by properties of the critical point. We use gauge-gravity duality to investigate the breakdown of diffusive hydrodynamics in two low temperature states dual to black holes with AdS$_2$ horizons, which exhibit quantum critical dynamics with an emergent scaling symmetry in time. We find that the breakdown is characterized by a collision between the diffusive pole of the retarded Green's function with a pole associated to the AdS$_2$ region of the geometry, such that the local equilibration time is set by infra-red properties of the theory. The absolute values of the frequency and wavevector at the collision ($ω_{eq}$ and $k_{eq}$) provide a natural characterization of all the low temperature diffusivities $D$ of the states via $D=ω_{eq}/k_{eq}^2$ where $ω_{eq}=2πΔT$ is set by the temperature $T$ and the scaling dimension $Δ$ of an operator of the infra-red quantum critical theory. We confirm that these relations are also satisfied in an SYK chain model in the limit of strong interactions. Our work paves the way towards a deeper understanding of transport in quantum critical phases.

hep-th↗

arXiv2021

Slow relaxation and diffusion in holographic quantum critical phases

The dissipative dynamics of strongly interacting systems are often characterised by the timescale set by the inverse temperature $τ_P\sim\hbar/(k_BT)$. We show that near a class of strongly interacting quantum critical points that arise in the infra-red limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime $τ_{eq}$ is parametrically longer than $τ_P$: $τ_{eq}\gg T^{-1}$. The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point. The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by $τ_{eq}$ rather than $τ_P$. We conjecture that there exists a long-lived, propagating collective mode with velocity $v_s$, and in this case the relation $D=v_s^2τ_{eq}$ holds exactly in the limit $Tτ_{eq}\gg1$. While scale invariance is broken, a generalised scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. Our work further underlines the connection between dangerously irrelevant deformations and slow equilibration.

hep-th↗

arXiv2020

Non-vanishing normal density in cold holographic superfluids

The low energy and finite temperature excitations of a $d+1$-dimensional system exhibiting superfluidity are well described by a hydrodynamic model with two fluid flows: a normal flow and a superfluid flow. In the vicinity of a quantum critical point, thermodynamics and transport in the system are expected to be controlled by the critical exponents and by the spectrum of irrelevant deformations away from the quantum critical point. Here, using gauge-gravity duality, we present the low temperature dependence of thermodynamic and charge transport coefficients at first order in the hydrodynamic derivative expansion in terms of the critical exponents. Special attention will be paid to the behavior of the charge density of the normal flow in systems with emergent infrared conformal and Lifshitz symmetries, parameterized by a Lifshitz dynamical exponent $z>1$. When $1\leq z 1$) previous results obtained by relativistic effective field theory techniques. Instead, when $z>d+2$, we show that the normal charge density becomes non-vanishing at zero temperature. An extended appendix generalizes these results to systems that violate hyperscaling as well as systems with generalized photon masses. Our results clarify previous work in the holographic literature and have relevance to recent experimental measurements of the superfluid density on cuprate superconductors.

hep-th↗

arXiv2020

Normal charge densities in quantum critical superfluids

The normal density of a translation-invariant superfluid often vanishes at zero temperature, as is observed in superfluid Helium and conventional superconductors described by BCS theory. Here we show that this need not be the case. We investigate the normal density in models of quantum critical superfluids using gauge-gravity duality. Models with an emergent infrared Lorentz symmetry lead to a vanishing normal density. On the other hand, models which break the isotropy between time and space may enjoy a non-vanishing normal density, depending on the spectrum of irrelevant deformations around the underlying quantum critical groundstate. Our results may shed light on recent measurements of the superfluid density and low energy spectral weight in superconducting overdoped cuprates.

hep-th↗

arXiv2020

Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points

The transport behavior of strongly anisotropic systems is significantly richer compared to isotropic ones. The most dramatic spatial anisotropy at a critical point occurs at a Lifshitz transition, found in systems with merging Dirac or Weyl point or near the superconductor-insulator quantum phase transition. Previous work found that in these systems a famous conjecture on the existence of a lower bound for the ratio of a shear viscosity to entropy is violated, and proposed a generalization of this bound for anisotropic systems near charge neutrality involving the electric conductivities. The present study uses scaling arguments and the gauge-gravity duality to confirm the previous analysis of universal bounds in anisotropic Dirac systems. We investigate the strongly-coupled phase of quantum Lifshitz systems in a gravitational Einstein-Maxwell-dilaton model with a linear massless scalar which breaks translations in the boundary dual field theory and sources the anisotropy. The holographic computation demonstrates that some elements of the viscosity tensor can be related to the ratio of the electric conductivities through a simple geometric ratio of elements of the bulk metric evaluated at the horizon, and thus obey a generalized bound, while others violate it. From the IR critical geometry, we express the charge diffusion constants in terms of the square butterfly velocities. The proportionality factor turns out to be direction-independent, linear in the inverse temperature, and related to the critical exponents which parametrize the anisotropic scaling of the dual field theory.

cond-mat.str-el↗

arXiv2019

Gapless and gapped holographic phonons

We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in arXiv:1812.08118 continues to hold in this model for weak enough explicit breaking.

hep-th↗

arXiv2019

Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states

We study thermodynamic and transport observables of quantum critical states that arise in the infra-red limit of holographic renormalisation group flows. Although these observables are expected to exhibit quantum critical scaling, there are a number of cases in which their frequency and temperature dependences are in apparent contradiction with scaling theories. We study two different classes of examples, and show in both cases that the apparent breakdown of scaling is a consequence of the dependence of observables on an irrelevant deformation of the quantum critical state. By assigning scaling dimensions to the near-horizon observables, we formulate improved scaling theories that are completely consistent with all explicit holographic results once the dependence on the dangerously irrelevant coupling is properly accounted for. In addition to governing thermodynamic and transport phenomena in these states, we show that the dangerously irrelevant coupling also controls late-time equilibration, which occurs at a rate parametrically slower than the temperature $1/τ_{eq}\ll T$. At very late times, transport is diffusion-dominated, with a diffusivity that can be written simply in terms of $τ_{eq}$ and the butterfly velocity, $D\sim v_B^2τ_{eq}$. We conjecture that in such cases there exists a long-lived, propagating collective mode with velocity $v_s$, and in this case the relation $D=v_s^2τ_{eq}$ holds exactly in the limit $τ_{eq} T\gg1$.

hep-th↗