Spatial modulation and conductivities in effective holographic theories

Abstract

We analyze a class of bottom-up holographic models for low energy thermoelectric transport. The models we focus on belong to a family of Einstein-Maxwell-dilaton theories parameterized by two scalar functions, characterizing the dilaton self-interaction and the gauge coupling function. We impose spatially inhomogeneous lattice boundary conditions for the dilaton on the AdS boundary and study the resulting phase structure attained at low energies. We find that as we dial the scalar functions at our disposal (changing thus the theory under consideration), we obtain either (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases. We chart out the domain where the incoherent metals appear in a restricted parameter space of theories. We also analyze the optical conductivity, noting that non-trivial scaling behaviour at intermediate frequencies appears to only be possible for very narrow regions of parameter space.

Hydrodynamic transport in strongly coupled disordered quantum field theories

“…It is also worth stressing that henceforth, when we refer to 'hydrodynamic' transport we refer to the transport equations being written in terms of (23) and (29). Remarkably, essentially all of our results rely only on the structure of these equations being obeyed, and not on  and  obeying thermodynamic Maxwell relationsholographic horizon fluids do not obey any obvious Maxwell relations.…”

“…This general framework readily generalizes to account for higher derivative corrections to hydrodynamics, if one wishes to directly include them, but we will not include them in this paper. Equation (23) and (29) are not wellposed until we include first order corrections to hydrodynamics, so it is necessary to work at least to this order in the gradient expansion.…”

“…More recently [29] has generalized the results of [28] to include the effects of a dynamical scalar field in the dual theory. In general this scalar must be consistently included within hydrodynamics, and so we must consider a more general theory to connect with these results in the generic case.…”

“…The second approach is holography [20][21][22], which reduces the computation of Green's functions to solving classical differential equations in a black hole background. This can be done numerically [23][24][25][26][27][28][29], though in some cases analytic insight can be obtained [26,[28][29][30][31][32][33][34][35], sometimes by employing the memory matrix method [8,36,37]. Surprisingly, many of the above transport theories from recent years completely match hydrodynamic predictions, at least superficially, despite being formally beyond the regime of validity of hydrodynamics.…”

Drude in D major

“…Some studies focus on configurations which describe a lattice in the dual field theory, for instance when the chemical potential is a periodic function of a spatial direction on the boundary. Gravitational solutions of this kind have been successfully constructed [1][2][3][4][5] and they indeed reproduce the expected low frequency dynamics, i.e. the zero frequency delta functions in the conductivities are resolved into finite width Drude peaks.…”