Abstract
We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.
Highlights
Dynamics predicted by these effective theories has been tested, in the appropriate regime, against holographic models and been found to concur with a great accuracy
First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field
Combining the results with the method outlined in [27, 33] we provide a closed form for the AC hydrodynamic correlators which depends solely on their
Summary
The equations of motion for the (almost-)conserved hydrodynamic charges are the conservation equations for the stress tensor and the charge current. For our system, which includes the presence of translation breaking scalar operators OI , these take the form. Where T μν = T μν is the stress tensor, F μν an external electromagnetic field strength, Jμ = Jμ a U(1) charge current and ΦI (x) are spatially modulated sources for the scalars OI. In addition we will need the “Josephson relation” which can be thought of as generating the evolution of the translation breaking scalars. This latter relation must be derived order by order in derivatives and doing so in the presence of an external magnetic field, and in the case of explicit breaking an additional non-zero phase relaxation, is one of the main thrusts of this section
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