Thermal conductivity at a disordered quantum critical point

Abstract

Strongly disordered and strongly interacting quantum critical points are difficult to access with conventional field theoretic methods. They are, however, both experimentally important and theoretically interesting. In particular, they are expected to realize universal incoherent transport. Such disordered quantum critical theories have recently been constructed holographically by deforming a CFT by marginally relevant disorder. In this paper we find additional disordered fixed points via relevant disordered deformations of a holographic CFT. Using recently developed methods in holographic transport, we characterize the thermal conductivity in both sets of theories in 1+1 dimensions. The thermal conductivity is found to tend to a constant at low temperatures in one class of fixed points, and to scale as $T^{0.3}$ in the other. Furthermore, in all cases the thermal conductivity exhibits discrete scale invariance, with logarithmic in temperature oscillations superimposed on the low temperature scaling behavior. At no point do we use the replica trick.

1+28 pages. 6 figures

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Cited by in corpus (14)

• Numerical Methods for Finding Stationary Gravitational Solutions
• Shear viscosity in holography and effective theory of transport without translational symmetry
• On holographic disorder-driven metal-insulator transitions
• Non-equilibrium fixed points of coupled Ising models
• Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance
• The renormalization group flow in field theories with quenched disorder
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Power Law of Shear Viscosity in Einstein-Maxwell-Dilaton-Axion model
• Renormalization group in quantum critical theories with Harris-marginal disorder
• Disordered quantum critical fixed points from holography
• Beyond Drude transport in hydrodynamic metals
• Noisy Branes
• Critical and near-critical relaxation of holographic superfluids
• Scalar Self-force for High Spin Black Holes