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arXiv:1506.02662 · New Journal of Physics

Hydrodynamic transport in strongly coupled disordered quantum field theories

Andrew Lucas

Published Oct 28, 2015• 79 citations
arXivHTMLPDF

Abstract

We compute direct current 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.

DOI
10.1088/1367-2630/17/11/113007

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We compute direct current 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.
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We model strange metals as quantum liquids without quasiparticle excitations, but with slow momentum relaxation and with slow diffusive dynamics of a conserved charge and energy. General expressions are obtained for electrical, thermal, and thermoelectric transport in the presence of an applied magnetic field using the memory matrix formalism. In the appropriate limits, our expressions agree with previous hydrodynamic and holographic results. We discuss the relationship of such results to thermoelectric and Hall transport measurements in the strange-metal phase of the hole-doped cuprates.
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The impact of lattice vibrations on the electric conductivity has been considered a settled issue since the proof of the Migdal theorem. The precondition for its validity is a higher velocity of electronic than phononic excitation modes. In some new materials, e. g. weakly coupled spin chains and heavy fermion systems, this precondition is not fulfilled. The heat conductivity of such systems is calculated by means of perturbation theory in this work. Another subject is the interplay of Umklapp scattering and weak disorder in spin chains and one-dimensional correlated metals. Hidden conservation laws lead to a strong coupling between heat current and charge or spin current, respectively. The transport properties are calculated perturbatively within the hydrodynamic memory matrix formalism, which gives a lower bound to the conductivies. To calculate the Lorenz number of one-dimensional metals, we model within this formalism also the influence of phonons, which in physical systems contribute substantially to the heat current. The introduction of ultracold quantum gases in optical lattices in the recent years provides a powerful tool for the modeling of many systems to solid state physics, in particular systems out of equilibrium. The relatively slow dynamics of the cold atoms allows for time resolved imaging of the atoms and thus opens up new perspectives. In the last part of this thesis, a recent experiment, which measures the expansion of a correlated atom cloud in an optical lattice, is compared to a lattice Boltzmann simulation. Depending on the local density, the problem is shown to be described by the crossover from diffusive to ballistic transport.
We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency ωωω, domains of size ξ∼D/ωξ\sim\sqrt{D/ω}ξ∼D/ω​ can be considered as internally thermal, but weakly coupled with each other. We calculate the transport coefficients to lowest order in the coupling, assuming incoherent transport between such domains. Our framework naturally captures the sub-leading non analytic corrections to the transport coefficients, known as hydrodynamic long time tails. In addition, it allows us to obtain a generalized relation between charge and thermal transport coefficients, in the spirit of the Wiedemann-Franz law. We verify our results, which satisfy several non-trivial consistency checks, via exact diagonalization studies on the one-dimensional extended Fermi-Hubbard model.
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