Incoherent transport for phases that spontaneously break translations

Aristomenis Donos,Vaios Ziogas,Tom Griffin,Jerome P Gauntlett

doi:10.1007/jhep04(2018)053

Aristomenis Donos, Vaios Ziogas + Show 2 more

Open Access

https://doi.org/10.1007/jhep04(2018)053

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Abstract

We consider phases of matter at finite charge density which spontaneously break spatial translations. Without taking a hydrodynamic limit we identify a boost invariant incoherent current operator. We also derive expressions for the small frequency behaviour of the thermoelectric conductivities generalising those that have been derived in a translationally invariant context. Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions.

Highlights

Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions
JHEP04(2018)053 incoherent current and argue that when there is no superfluid the low frequency behaviour of the thermoelectric conductivities can still be expressed in terms of certain thermodynamics quantities as well as the finite incoherent DC conductivity, [σinc]DC
Within a holographic context, describing a strongly coupled system, we explain how [σinc]DC can be calculated in terms of a Stokes flow on the spatially modulated black hole horizon, supplemented with some thermodynamic quantities of the background

Summary

Boost invariant incoherent current

Consider a relativistic quantum field theory at finite temperature defined on flat spacetime. Defining the total charge density ρ ≡ Jt , the total energy density ε ≡ − Ttt , and the total entropy density s, we have the fundamental thermodynamic relation T s + ρμ = ε + p It was shown in [5] that the zero mode of the heat current must vanish, Qi = 0, where we recall that Qi ≡ −T it − μJi. If the global U(1) symmetry is not spontaneously broken, which will be the principle focus of this paper, by extending the arguments of [5], we can invoke invariance under large gauge transformations with gauge parameter Λ = xi qi to argue that Ji = 0 as well. We note that the second term vanishes as ω → 0

Holography

A Non-thermodynamically preferred phases

B Bulk non-uniqueness

C Perturbative lattice