arXiv subjects

Andrew Lucas

Publications and source records attributed to Andrew Lucas.

At least 109 records · Page 6Linked to original sources

arXiv2019

Finite speed of quantum scrambling with long range interactions

In a locally interacting many-body system, two isolated qubits, separated by a large distance $r$, become correlated and entangled with each other at a time $t \ge r/v$. This finite speed $v$ of quantum information scrambling limits quantum information processing, thermalization and even equilibrium correlations. Yet most experimental systems contain long range power law interactions -- qubits separated by $r$ have potential energy $V(r)\propto r^{-α}$. Examples include the long range Coulomb interactions in plasma ($α=1$) and dipolar interactions between spins ($α=3$). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large $α$. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors.

quant-ph↗

arXiv2019

Electron hydrodynamics with a polygonal Fermi surface

Recent experiments have observed hints of hydrodynamic electron flow in a number of materials, not all of which have an isotropic Fermi surface. We revisit these experiments in $\mathrm{PdCoO}_2$, a quasi-two-dimensional material whose Fermi surface is a rounded hexagon, and observe that the data appears quantitatively consistent with a non-hydrodynamic interpretation. Nevertheless, motivated by such experiments, we develop a simple model for the low temperature kinetics and hydrodynamics of a two-dimensional Fermi liquid with a polygonal Fermi surface. A geometric effect leads to a finite number of additional long-lived quasihydrodynamic "imbalance" modes and corresponding qualitative changes in transport at the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, we find incoherent diffusion and a new dissipative component of the viscosity tensor arising from the explicit breaking of rotational invariance by the Fermi surface. Finally, we compute the conductance of narrow channels across the ballistic-to-hydrodynamic crossover and demonstrate a modification of the Gurzhi effect that allows for non-monotonic temperature and width dependence in the channel conductance.

cond-mat.str-el↗

arXiv2019

Operator size at finite temperature and Planckian bounds on quantum dynamics

It has long been believed that dissipative time scales $τ$ obey a "Planckian" bound $τ\gtrsim \frac{\hbar}{k_{\mathrm{B}}T}$ in strongly coupled quantum systems. Despite much circumstantial evidence, however, there is no known $τ$ for which this bound is universal. Here we define operator size at finite temperature, and conjecture such a $τ$: the time scale over which small operators become large. All known many-body theories are consistent with this conjecture. This proposed bound explains why previously conjectured Planckian bounds do not always apply to weakly coupled theories, and how Planckian time scales can be relevant to both transport and chaos.

cond-mat.str-el↗

arXiv2019

Holography and hydrodynamics with weakly broken symmetries

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 as quasihydrodynamics. Examples of quasihydrodynamics are numerous, with the most transparent among them hydrodynamics with weakly broken translational symmetry. Here, we show how a number of other theories, normally not thought of in this context, can also be understood within a broader framework of quasihydrodynamics: in particular, the Müller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields. While historical formulations of quasihydrodynamic theories were typically highly phenomenological, here, we develop a holographic formalism to systematically derive such theories from a (microscopic) dual gravitational description. Beyond laying out a general holographic algorithm, we show how the Müller-Israel-Stewart theory can be understood from a dual higher-derivative gravity theory and magnetohydrodynamics from a dual theory with two-form bulk fields. In the latter example, this allows us to unambiguously demonstrate the existence of dynamical photons in the holographic description of magnetohydrodynamics.

hep-th↗

arXiv2019

Fast scrambling on sparse graphs

Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb-Robinson bounds, generalized Sachdev-Ye-Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity. These models also elucidate how quantum chaos is not universally related to scrambling: we construct random few-body circuits with infinite Lyapunov exponent but logarithmic scrambling time. We discuss analogies between quantum models on graphs and quantum black holes, and suggest methods to experimentally study scrambling with as many as 100 sparsely-connected quantum degrees of freedom.

cond-mat.str-el↗

arXiv2019

Quantum many-body dynamics on the star graph

We study 2-local Hamiltonian quantum systems, consisting of qubits interacting on the star graph of N vertices. We numerically demonstrate that these models are generically non-integrable at infinite temperature, and find evidence for a finite temperature phase transition to a glassy phase in generic models. Operators can become complicated in constant time: we explicitly find that there is no bound on out-of-time-ordered correlators, even at finite temperature. Operator growth is not correctly modeled by stochastic quantum dynamics, including Brownian Hamiltonian dynamics or random unitary circuits. The star graph (and similar constructions) may serve as a useful testing ground for conjectures about universality, quantum chaos and Planckian dissipation in k-local systems, including in experimental quantum simulators.

cond-mat.str-el↗

arXiv2019

Emergent entropy production and hydrodynamics in quantum many-body systems

We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy. This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime. We find the absence of non-hydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium. The observable part of the microscopic entropy obeys the local second law of thermodynamics, and quantitatively agrees with the phenomenological predictions of hydrodynamics. Our approach naturally generalizes to ergodic systems with additional symmetries, may lead to numerical algorithms to calculate diffusion constants for lattice models, and implies sufficiency conditions for a rigorous derivation of hydrodynamics in quantum systems.

cond-mat.stat-mech↗

arXiv2018

Hard combinatorial problems and minor embeddings on lattice graphs

Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling constants. Secondly, the interaction graph of the QUBO must have an effective minor embedding into a two-dimensional nonplanar lattice graph. We describe new strategies for constructing QUBOs for NP-complete/hard combinatorial problems that address both of these challenges. Our results include asymptotically improved embeddings for number partitioning, filling knapsacks, graph coloring, and finding Hamiltonian cycles. These embeddings can be also be found with reduced computational effort. Our new embedding for number partitioning may be more effective on next-generation hardware.

quant-ph↗

arXiv2018

Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals

We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity can be parametrically smaller than predicted by the Wiedemann-Franz law. A less severe violation of the Mott law arises. We quantitatively compare the violations of the Wiedemann-Franz law arising from (i) momentum-conserving electron-electron scattering in the collision integral, (ii) hydrodynamic modifications of the electron-impurity scattering rate, and (iii) thermal broadening of the Fermi surface, and show that (i) is the largest. We present simple formulas for electrical and thermal magnetoconductivity across the ballistic-to-hydrodynamic limit, along with a more complicated formula for the thermoelectric magnetoconductivity. In a finite magnetic field, the Lorenz number may be smaller or larger than predicted by the Wiedemann-Franz law, and the crossover between these behaviors is a clear prediction for experiments. The arbitrarily strong violation of the Wiedemann-Franz law found in our work arises entirely from electron-electron interaction effects within the Fermi liquid paradigm, and does not imply any non-Fermi liquid behavior. We predict clear experimental signatures of bulk hydrodynamics in high-mobility 2D GaAs semiconductor structures, where failure of the Wiedemann-Franz law should persist down to very low temperatures in high-quality, low-density samples.

cond-mat.str-el↗

arXiv2018

Electronic sound modes and plasmons in hydrodynamic two-dimensional metals

Using an analytically tractable kinetic model of a two dimensional Fermi liquid of electrons, we characterize the crossovers between zero sound, first sound and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects, up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two dimensional electron gases.

cond-mat.str-el↗

arXiv2018

Holographic quantum matter

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

hep-th↗

arXiv2018

Dyakonov-Shur instability across the ballistic-to-hydrodynamic crossover

We numerically solve semiclassical kinetic equations and compute the growth rate of the Dyakonov-Shur instability of a two-dimensional Fermi liquid in a finite length cavity. When electron-electron scattering is fast, we observe the well-understood hydrodynamic instability, and its disappearance due to viscous dissipation. When electron-electron scattering is negligible, we find that the instability re-emerges for certain boundary conditions, but not for others. We discuss the implications of these findings for experiments.

cond-mat.str-el↗

arXiv2018

Kinetic theory of electronic transport in random magnetic fields

We present the theory of quasiparticle transport in perturbatively small inhomogeneous magnetic fields across the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, the resistivity $ρ$ generically grows proportionally to the rate of momentum-conserving electron-electron collisions at large enough temperatures $T$. In particular, the resulting flow of electrons provides a simple scenario where viscous effects suppress conductance below the ballistic value. This new mechanism for $ρ\propto T^2$ resistivity in a Fermi liquid may describe low $T$ transport in single-band $\mathrm{SrTiO}_3$.

cond-mat.str-el↗

arXiv2018

Hydrodynamics of electrons in graphene

Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the "phase diagram" of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.

cond-mat.str-el↗

arXiv2018

Kinetic theory of transport for inhomogeneous electron fluids

The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of unconventional metals. When quasiparticles are long-lived, one can account for these intertwined effects by solving spatially inhomogeneous Boltzmann equations. Assuming smooth disorder and neglecting umklapp scattering, we solve these inhomogeneous kinetic equations and compute the electrical resistivity across the ballistic-to-hydrodynamic transition. An important consequence of electron-electron interactions is the modification of the momentum relaxation time; this effect is ignored in the conventional theory. We characterize precisely when interactions enhance the momentum scattering rate, and when they decrease it. Our approach unifies existing semiclassical theories of transport and reveals novel transport mechanisms. In particular, we explain how the resistivity can be proportional to the rate of momentum-conserving collisions. We compare this result with existing transport mysteries, including the disorder-independent $T^2$ resistivity of many Fermi liquids, and the linear-in-$T$ "Planckian-limited" resistivity of many strange metals.

cond-mat.str-el↗

arXiv2017

Constraints on hydrodynamics from many-body quantum chaos

Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. In this work, we identify a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly effect leads to upper bounds on the speed of sound and diffusion constants of hydrodynamics. These bounds link two very different theories of quantum many-body dynamics, clarify the relationship between classical hydrodynamics and quantum information loss, and provide a simple way to constrain theories of thermalization and quantum chaos in experiments.

hep-th↗

arXiv2017

Origin of the Drude peak and of zero sound in probe brane holography

At zero temperature, the charge current operator appears to be conserved, within linear response, in certain holographic probe brane models of strange metals. At small but finite temperature, we analytically show that the weak non-conservation of this current leads to both a collective "zero sound" mode and a Drude peak in the electrical conductivity. This simultaneously resolves two outstanding puzzles about probe brane theories. The nonlinear dynamics of the current operator itself appears qualitatively different.

hep-th↗

arXiv2017

Hydrodynamic charge and heat transport on inhomogeneous curved spaces

We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects, and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential, and discuss the extent to which our hydrodynamic theory is relevant for experimentally realizable condensed matter systems, including suspended graphene at the Dirac point.

cond-mat.str-el↗