Abstract
We analyze a class of bottom-up holographic models for low energy thermo-electric 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.
Highlights
We take a bottom up, phenomenological approach to holography, and following [6, 24, 25] we choose a model with the minimal ingredients necessary to calculate conductivities in a 2+1 dimensional quantum critical theory
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 find that as we dial the scalar functions at our disposal, we obtain either (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases
Summary
We take a bottom up, phenomenological approach to holography, and following [6, 24, 25] we choose a model with the minimal ingredients necessary to calculate conductivities in a 2+1 dimensional quantum critical theory. In doing so we choose to fix the potential to have a Taylor expansion around the origin of field space of the form V (Φ) = Φ2 + · · · This choice corresponds to an effective conformal mass term m2 = −2 for the scalar ensuring that we have simple fall-offs (with non-normalizable and normalizable being z and z2 respectively asymptotically). As we explain below the presence of radially conserved quantities in the theory mean that a great deal about the linear response functions, and the phase of the dual field theory, may be extracted from knowledge of the near horizon geometry Given these boundary conditions, a suitable metric ansatz for the investigation of these inhomogeneous phases is [6]: ds. While such investigations are interesting we postpone the construction of such solutions and the investigation of their thermodynamic and transport properties to future work, and focus below on constructing solutions sourced by the single harmonic cos(kx)
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