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We develop a general hydrodynamic framework for computing direct currentthermal and electric transport in a strongly interacting finite temperaturequantum system near a Lorentz-invariant quantum critical point. Our frameworkis non-perturbative in the strength of long wavelength fluctuations in thebackground charge density of the electronic fluid, and requires the rate ofelectron-electron scattering to be faster than the rate of electron-impurityscattering. We use this formalism to compute transport coefficients in theDirac fluid in clean samples of graphene near the charge neutrality point, andfind results insensitive to long range Coulomb interactions. Numerical resultsare compared to recent experimental data on thermal and electrical conductivityin the Dirac fluid in graphene and substantially improved quantitativeagreement over existing hydrodynamic theories is found. We comment on theinterplay between the Dirac fluid and acoustic and optical phonons, andqualitatively explain experimentally observed effects. Our work paves the wayfor quantitative contact between experimentally realized condensed mattersystems and the wide body of high energy inspired theories on transport ininteracting many-body quantum systems.

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