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.
Highlights
As such is often not especially privileged
In this paper we find additional disordered fixed points via relevant disordered deformations of a holographic conformal field theory (CFT)
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
Summary
As such is often not especially privileged. in the absence of quasiparticles, but in the presence of translation invariance, momentum conservation dominates the late time behavior of heat current excitations. If the low energy physics is described by an IR fixed point with an emergent long wavelength translation invariance (as is the case whenever the low energy dynamics admits an effective gapless QFT description), the memory matrix tells us that the dc thermal conductivity is controlled by the leading irrelevant operator that breaks translation invariance [4,5,6]. Transport in these cases is solved in principle, up to the characterization of the leading irrelevant operator for a given system. Since these fixed points are found in perturbation theory, transport will be described by a quasiparticle-based Boltzmann equation, and will not access the strongly interacting and strongly disordered regimes we are interested in
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