*Phys Rev Lett ; 125(4): 041601, 2020 Jul 24.*

##### RESUMO

Large N matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology. In this approach, operator expectation values are related by symmetries-such as time translation and SU(N) gauge invariance-and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large N single matrix quantum mechanics. Finally, we present new results on the ground state of large N two matrix quantum mechanics.

*Proc Natl Acad Sci U S A ; 117(6): 2852-2857, 2020 Feb 11.*

##### RESUMO

The bilayer perovskite Sr3Ru2O7 has been widely studied as a canonical strange metal. It exhibits T-linear resistivity and a T log(1/T) electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in "hot" Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, "cold" Fermi surfaces scatter into one hot and one cold electron renders the ostensibly noncritical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a 2D van Hove singularity explains the anomalous transport observed in strained Sr2RuO4.

*Phys Rev Lett ; 122(18): 186601, 2019 May 10.*

##### RESUMO

Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.

*Phys Rev Lett ; 122(9): 091602, 2019 Mar 08.*

##### RESUMO

The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of nonlinear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point halfway to the diffusive pole, at frequency ω=-(i/2)Dk^{2}. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

*Phys Rev Lett ; 121(17): 170601, 2018 Oct 26.*

##### RESUMO

We prove an upper bound on the diffusivity of a dissipative, local, and translation invariant quantum Markovian spin system: D≤D_{0}+(αv_{LR}τ+ßξ)v_{C}. Here v_{LR} is the Lieb-Robinson velocity, v_{C} is a velocity defined by the current operator, τ is the decoherence time, ξ is the range of interactions, D_{0} is a decoherence-induced microscopic diffusivity, and α and ß are precisely defined dimensionless coefficients. The bound constrains quantum transport by quantities that can either be obtained from the microscopic interactions (D_{0}, v_{LR}, v_{C}, ξ) or else determined from independent local nontransport measurements (τ, α, ß). We illustrate the general result with the case of a spin-half XXZ chain with on-site dephasing. Our result generalizes the Lieb-Robinson bound to constrain the sub-ballistic diffusion of conserved densities in a dissipative setting.

*Phys Rev Lett ; 119(14): 141601, 2017 Oct 06.*

##### RESUMO

The linear growth of operators in local quantum systems leads to an effective light cone even if the system is nonrelativistic. We show that the consistency of diffusive transport with this light cone places an upper bound on the diffusivity: Dâ²v^{2}τ_{eq}. The operator growth velocity v defines the light cone, and τ_{eq} is the local equilibration time scale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models, this bound establishes a relation between the hydrodynamic and leading nonhydrodynamic quasinormal modes of planar black holes. Our bound relates transport data-including the electrical resistivity and the shear viscosity-to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed T-linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma, and the spin transport of unitary fermions.

*Proc Natl Acad Sci U S A ; 114(43): 11344-11349, 2017 10 24.*

##### RESUMO

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

*Proc Natl Acad Sci U S A ; 114(21): 5378-5383, 2017 05 23.*

##### RESUMO

The thermal diffusivity in the [Formula: see text] plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25-300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron-phonon "soup" picture characterized by a diffusion constant [Formula: see text], where [Formula: see text] is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time [Formula: see text].

*Science ; 355(6323): 371-374, 2017 01 27.*

##### RESUMO

In electrically conductive solids, the Wiedemann-Franz law requires the electronic contribution to thermal conductivity to be proportional to electrical conductivity. Violations of the Wiedemann-Franz law are typically an indication of unconventional quasiparticle dynamics, such as inelastic scattering, or hydrodynamic collective motion of charge carriers, typically pronounced only at cryogenic temperatures. We report an order-of-magnitude breakdown of the Wiedemann-Franz law at high temperatures ranging from 240 to 340 kelvin in metallic vanadium dioxide in the vicinity of its metal-insulator transition. Different from previously established mechanisms, the unusually low electronic thermal conductivity is a signature of the absence of quasiparticles in a strongly correlated electron fluid where heat and charge diffuse independently.

*Phys Rev Lett ; 115(12): 121602, 2015 Sep 18.*

##### RESUMO

To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.

*Phys Rev Lett ; 112(23): 231601, 2014 Jun 13.*

##### RESUMO

We deform conformal field theories with classical gravity duals by marginally relevant random disorder. We show that the disorder generates a flow to IR fixed points with a finite amount of disorder. The randomly disordered fixed points are characterized by a dynamical critical exponent z > 1 that we obtain both analytically (via resummed perturbation theory) and numerically (via a full simulation of the disorder). The IR dynamical critical exponent increases with the magnitude of disorder, probably tending to z â ∞ in the limit of infinite disorder.

*Phys Rev Lett ; 108(24): 241601, 2012 Jun 15.*

##### RESUMO

Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature dc 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 Γâ¼T2. 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 Γâ¼T(2Δ(k(L))). Here Δ(k(L))≥0 is the dimension of the (irrelevant or marginal) charge density operator J(t)(ω,k(L)) in the locally critical theory, at the lattice momentum k(L). We illustrate this result with an explicit computation in locally critical theories described holographically via Einstein-Maxwell theory in Anti-de Sitter spacetime. We furthermore show that scattering by random impurities in these locally critical theories gives a universal Γâ¼(log(1/T))(-1).

*Phys Rev Lett ; 106(12): 121601, 2011 Mar 25.*

##### RESUMO

We show that charged black holes in anti-de Sitter spacetime can undergo a third-order phase transition at a critical temperature in the presence of charged fermions. In the low temperature phase, a fraction of the charge is carried by a fermion fluid located a finite distance from the black hole. In the zero temperature limit, the black hole is no longer present and all charge is sourced by the fermions. The solutions exhibit the low temperature entropy density scaling s~T(2/z) anticipated from the emergent IR criticality of recently discussed electron stars.

*Phys Rev Lett ; 101(3): 031601, 2008 Jul 18.*

##### RESUMO

We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (dc) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.

*Phys Rev Lett ; 98(11): 111601, 2007 Mar 16.*

##### RESUMO

It is observed that strings in AdS(5) x S(5) and membranes in AdS(7) x S(4) exhibit long range phase interactions. Two well separated membranes dragged around one another in anti-de Sitter space (AdS) acquire phases of 2 pi/N. The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual field theory.