The Lorenz ratio as a guide to scattering contributions to transport in strongly correlated metals.

In many physical situations in which many-body assemblies exist at temperature , a characteristic quantum-mechanical time scale of approximately [Formula: see text] can be identified in both theory and experiment, leading to speculation that it may be the shortest meaningful time in such circumstances. This behavior can be investigated by probing the scattering rate of electrons in a broad class of materials often referred to as "strongly correlated metals". It is clear that in some cases only electron-electron scattering can be its cause, while in others it arises from high-temperature scattering of electrons from quantized lattice vibrations, i.

Bootstrapping Matrix Quantum Mechanics.

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.

Theory of the strange metal SrRuO.

The bilayer perovskite SrRuO has been widely studied as a canonical strange metal. It exhibits -linear resistivity and a log(1/) 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.

Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La Ba CuO.

Charge order is universal among high- cuprates, but its relation to superconductivity is unclear. While static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. Using time-resolved resonant soft x-ray scattering at a free-electron laser, we show that the charge order in prototypical La Ba CuO exhibits transverse fluctuations at picosecond time scales.

Bad Metallic Transport in a Modified Hubbard Model.

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.

Theory of Diffusive Fluctuations.

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.

Locality Bound for Dissipative Quantum Transport.

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+βξ)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 β 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, β).

Resistivity bound for hydrodynamic bad metals.

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.

Upper Bound on Diffusivity.

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: D≲v^{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.

Anomalous thermal diffusivity in underdoped YBaCuO.

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.

Anomalously low electronic thermal conductivity in metallic vanadium dioxide.

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.

Entanglement Entropy in Two-Dimensional String Theory.

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.

Disordered horizons: holography of randomly disordered fixed points.

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).

Locally critical resistivities from umklapp scattering.

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 Γ∼T2. We observe that local criticality, in which energies scale but momenta do not, provides a distinct route to efficient umklapp scattering.

Electron star birth: a continuous phase transition at nonzero density.

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.

Building a holographic superconductor.

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.

Anyonic strings and membranes in anti-de Sitter space and dual Aharonov-Bohm effects.

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.