arXiv subjects

Andrew Lucas

Publications and source records attributed to Andrew Lucas.

At least 127 records · Page 7Linked to original sources

arXiv2017

Spread of entanglement in a Sachdev-Ye-Kitaev chain

We study the spread of Rényi entropy between two halves of a Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield double (TFD) state. The SYK chain model is a model of chaotic many-body systems, which describes a one-dimensional lattice of Majorana fermions, with spatially local random quartic interaction. We find that for integer Rényi index $n>1$, the Rényi entanglement entropy saturates at a parametrically smaller value than expected. This implies that the TFD state of the SYK chain does not rapidly thermalize, despite being maximally chaotic: instead, it rapidly approaches a prethermal state. We compare our results to the signatures of thermalization observed in other quenches in the SYK model, and to intuition from nearly-$\mathrm{AdS}_2$ gravity.

hep-th↗

arXiv2017

Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains

We compute the energy diffusion constant $D$, Lyapunov time $τ_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong coupling limit. We find $D\le v_{\text{B}}^2 τ_{\text{L}}$ from a combination of analytical and numerical approaches. Our example necessitates the sharpening of postulated transport bounds based on quantum chaos.

hep-th↗

arXiv2017

Quantum critical response: from conformal perturbation theory to holography

We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high frequencies. Knowledge of the high frequency response allows us then to derive non-perturbative sum rules. We show, via explicit computations, how holography recovers the general results of CFT, and the associated sum rules, for any holographic field theory with a conformal UV completion -- regardless of any possible new ordering and/or scaling physics in the IR. We numerically obtain holographic response functions at all frequencies, allowing us to probe the breakdown of the asymptotic high-frequency regime. Finally, we show that high frequency response functions in holographic Lifshitz theories are quite similar to their conformal counterparts, even though they are not strongly constrained by symmetry.

hep-th↗

arXiv2017

Resistivity bound for hydrodynamic bad metals

We obtain a rigorous upper bound on the resistivity $ρ$ of an electron fluid whose electronic mean free path is short compared to the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a non-thermal diffusion process -- such as an imbalance mode between different bands -- we show that the resistivity bound becomes $ρ\lesssim A \, Γ$. The coefficient $A$ is independent of temperature and inhomogeneity lengthscale, and $Γ$ is a microscopic momentum-preserving scattering rate. In this way we obtain a unified and novel mechanism -- without umklapp -- for $ρ\sim T^2$ in a Fermi liquid and the crossover to $ρ\sim T$ in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides and heavy fermion compounds and has presented a longstanding challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.

cond-mat.str-el↗

arXiv2017

Magnetoresistance in relativistic hydrodynamics without anomalies

We present expressions for the magnetoconductivity and the magnetoresistance of a strongly interacting metal in 3+1 dimensions, derivable from relativistic hydrodynamics. Such an approach is suitable for ultraclean metals with emergent Lorentz invariance. When this relativistic fluid contains chiral anomalies, it is known to exhibit longitudinal negative magnetoresistance. We show that similar effects can arise in non-anomalous relativistic fluids due to the distinctive gradient expansion. In contrast with a Galilean-invariant fluid, the resistivity tensor of a dirty relativistic fluid exhibits similar angular dependence to negative magnetoresistance, even when the constitutive relations and momentum relaxation rate are isotropic. We further account for the effect of magnetic field-dependent corrections to the gradient expansion and the effects of long-wavelength impurities on magnetoresistance. We note that the holographic D3/D7 system exhibits negative magnetoresistance.

hep-th↗

arXiv2017

Stokes paradox in electronic Fermi liquids

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.

cond-mat.mes-hall↗

arXiv2017

Dynamical response near quantum critical points

We study high frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from conformal field theory allow us to fix the high frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality, and numerically via Quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high frequency optical conductivity, and the corresponding sum rule.

cond-mat.str-el↗

arXiv2016

Charge diffusion and the butterfly effect in striped holographic matter

Recently, it has been proposed that the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength "hydrodynamic" disorder in a single spatial direction. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.

hep-th↗

arXiv2016

Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals

We present a theory of thermoelectric transport in weakly disordered Weyl semimetals where the electron-electron scattering time is faster than the electron-impurity scattering time. Our hydrodynamic theory consists of relativistic fluids at each Weyl node, coupled together by perturbatively small inter-valley scattering, and long-range Coulomb interactions. The conductivity matrix of our theory is Onsager reciprocal and positive-semidefinite. In addition to the usual axial anomaly, we account for the effects of a distinct, axial-gravitational anomaly expected to be present in Weyl semimetals. Negative thermal magnetoresistance is a sharp, experimentally accessible signature of this axial-gravitational anomaly, even beyond the hydrodynamic limit.

cond-mat.str-el↗

arXiv2016

Shock waves, rarefaction waves and non-equilibrium steady states in quantum critical systems

We re-examine the emergence of a universal non-equilibrium steady state following a local quench between quantum critical heat baths in spatial dimensions greater than one. We show that energy transport proceeds by the formation of an instantaneous shock wave and a broadening rarefaction wave on either side of the interface, and not by two shock waves as previously proposed. For small temperature differences the universal steady state energy currents of the two-shock and rarefaction-shock solutions coincide. Over a broad range of parameters, the difference in the energy flow across the interface between these two solutions is at the level of two percent. The properties of the energy flow remain fully universal and independent of the microscopic theory. We briefly discuss the width of the shock wave in a viscous fluid, the effects of momentum relaxation, and the generalization to charged fluids.

hep-th↗

arXiv2016

Sound waves and resonances in electron-hole plasma

Inspired by the recent experimental signatures of relativistic hydrodynamics in graphene, we investigate theoretically the behavior of hydrodynamic sound modes in such quasi-relativistic fluids near charge neutrality, within linear response. Locally driving an electron fluid at a resonant frequency to such a sound mode can lead to large increases in the electrical response at the edges of the sample, a signature which cannot be explained using diffusive models of transport. We discuss the robustness of this signal to various effects, including electron-acoustic phonon coupling, disorder, and long-range Coulomb interactions. These long range interactions convert the sound mode into a collective plasmonic mode at low frequencies unless the fluid is charge neutral. At the smallest frequencies, the response in a disordered fluid is quantitatively what is predicted by a "momentum relaxation time" approximation. However, this approximation fails at higher frequencies (which can be parametrically small), where the classical localization of sound waves cannot be neglected. Experimental observation of such resonances is a clear signature of relativistic hydrodynamics, and provides an upper bound on the viscosity of the electron-hole plasma.

cond-mat.str-el↗

arXiv2016

Conductivity bounds in probe brane models

We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is introduced entirely through an inhomogeneous background charge density, we find simple lower and upper bounds on the electrical conductivity in arbitrary dimensions. In field theories in two spatial dimensions, we show that both bounds persist even when disorder is included in the bulk metric. We discuss the challenges with finding sharp lower bounds on conductivity in three or more spatial dimensions when the metric is inhomogeneous.

hep-th↗

arXiv2016

Incoherent thermal transport from dirty black holes

We study thermal transport in strongly disordered, strongly interacting quantum field theories without quasiparticles using gauge-gravity duality. We analyze linear perturbations of black holes with broken translational symmetry in Einstein-Maxwell-dilaton theories of gravity. Using general geometric arguments in the bulk, we derive bounds on thermal conductivity for the dual disordered field theories in one and two spatial dimensions. In the latter case, the thermal conductivity is always non-zero at finite temperature, so long as the dilaton potential is bounded from below. Hence, generic holographic models make non-trivial predictions about the thermal conductivity in a strongly disordered, strongly coupled metal in two spatial dimensions.

hep-th↗

arXiv2016

Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene

We develop a general hydrodynamic framework for computing direct current thermal and electric transport in a strongly interacting finite temperature quantum system near a Lorentz-invariant quantum critical point. Our framework is non-perturbative in the strength of long wavelength fluctuations in the background charge density of the electronic fluid, and requires the rate of electron-electron scattering to be faster than the rate of electron-impurity scattering. We use this formalism to compute transport coefficients in the Dirac fluid in clean samples of graphene near the charge neutrality point, and find results insensitive to long range Coulomb interactions. Numerical results are compared to recent experimental data on thermal and electrical conductivity in the Dirac fluid in graphene and substantially improved quantitative agreement over existing hydrodynamic theories is found. We comment on the interplay between the Dirac fluid and acoustic and optical phonons, and qualitatively explain experimentally observed effects. Our work paves the way for quantitative contact between experimentally realized condensed matter systems and the wide body of high energy inspired theories on transport in interacting many-body quantum systems.

cond-mat.str-el↗

arXiv2015

Absence of disorder-driven metal-insulator transitions in simple holographic models

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to Einstein-Maxwell theory in an asymptotically $\mathrm{AdS}_4$ spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond non-perturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

hep-th↗

arXiv2015

Hydrodynamic transport in strongly coupled disordered quantum field theories

We compute direct current (dc) thermoelectric transport coefficients in strongly coupled quantum field theories without long lived quasiparticles, at finite temperature and charge density, and disordered on long wavelengths compared to the length scale of local thermalization. Many previous transport computations in strongly coupled systems are interpretable hydrodynamically, despite formally going beyond the hydrodynamic regime. This includes momentum relaxation times previously derived by the memory matrix formalism, and non-perturbative holographic results; in the latter case, this is subject to some important subtleties. Our formalism may extend some memory matrix computations to higher orders in the perturbative disorder strength, as well as give valuable insight into non-perturbative regimes. Strongly coupled metals with quantum critical contributions to transport generically transition between coherent and incoherent metals as disorder strength is increased at fixed temperature, analogous to mean field holographic treatments of disorder. From a condensed matter perspective, our theory generalizes the resistor network approximation, and associated variational techniques, to strongly interacting systems where momentum is long lived.

hep-th↗

arXiv2015

The NEOWISE-Discovered Comet Population and the CO+CO2 production rates

The 163 comets observed during the WISE/NEOWISE prime mission represent the largest infrared survey to date of comets, providing constraints on dust, nucleus sizes, and CO+CO2 production. We present detailed analyses of the WISE/NEOWISE comet discoveries, and discuss observations of the active comets showing 4.6 $μ$m band excess. We find a possible relation between dust and CO+CO2 production, as well as possible differences in the sizes of long and short period comet nuclei.

astro-ph.EP↗

arXiv2015

Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

Interactions between particles in quantum many-body systems can lead to collective behavior described by hydrodynamics. One such system is the electron-hole plasma in graphene near the charge neutrality point which can form a strongly coupled Dirac fluid. This charge neutral plasma of quasi-relativistic fermions is expected to exhibit a substantial enhancement of the thermal conductivity, due to decoupling of charge and heat currents within hydrodynamics. Employing high sensitivity Johnson noise thermometry, we report the breakdown of the Wiedemann-Franz law in graphene, with a thermal conductivity an order of magnitude larger than the value predicted by Fermi liquid theory. This result is a signature of the Dirac fluid, and constitutes direct evidence of collective motion in a quantum electronic fluid.

cond-mat.mes-hall↗