From black holes to strange metals

Abstract

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory.Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

Charge transport by holographic Fermi surfaces

“…In particular we find for ν = 1 2 , which corresponds to MFL, the linear-T resistivity is recovered. A summary of the qualitative scaling behavior has been presented earlier in [17]. Here we provide a systematic exposition of the rather intricate calculation behind them and also give the numerical prefactors.…”

“…While it is fascinating that this set of results is self-consistent, we do stress that the marginal ν kF = 1 2 point is not special from our gravity treatment, and more work needs to be done to understand if there is a way to single it out in holography. 17 by N the dimension of the bulk spinor representation; in the case that d is odd we have N = 2 d+1 2 . Our treatment will essentially apply to any asymptotically AdS spacetime with planar slicing and a horizon in the interior; the criterion of asymptotically AdS is important only in the precise choice of UV boundary conditions and can be easily modified if necessary.…”

“…It can be understood as follows. Start with a uniform charge density at rest and in equilibrium, in a 17 See [51,78] for recent work in this direction. frame where j t ≡ ρ = 0, T tt = ǫ = 0, T ii = P, j i = 0, π i ≡ T ti = 0 ;…”

“…There is one surprise in the numerical results for the prefactors: for certain parameters of the bulk model (codimension one in parameter space), the leading contribution to the DC and optical conductivities vanishes, i.e. the actual conductivities are higher order in temperature than that presented [17]. This happens because the effective vertex determining the coupling between the fermionic operator and the external DC gauge field vanishes at leading order.…”

“…Recently, techniques from the AdS/CFT correspondence [12] have been used to find a class of non-Fermi liquids [13][14][15][16][17][18] (for a review see [19]). The low energy behavior of these non-Fermi liquids was shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the time direction.…”