Linear and quadratic in temperature resistivity from holography

Ge, Xian-Hui; Tian, Yu; Wu, Shang-Yu; Wu, Shuang-Qing

doi:10.1007/jhep11(2016)128

Cited by 33 publications

(45 citation statements)

References 90 publications

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“…The DC transport coefficients in this general background are given in section 5. The more detail derivation of the DC transport coefficients in this background was obtained in [69,71] (see also [72][73][74][75][76] for more recent work).…”

Section: The General Formalismmentioning

confidence: 99%

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Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Sin

Tian

et al. 2018

J. High Energ. Phys.

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We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ black hole is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension d, exponents z and θ. Remarkably, the case d = θ and z = 2 is a very special in that the charge diffusion D c is a constant and the energy diffusion D e might be ill-defined, but v 2 B τ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

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Section: The General Formalismmentioning

confidence: 99%

“…of transport coefficients of Lifshitz spacetime to those of the AdS geometry. Assuming the charge current induced by the auxiliary gauge field is vanishing J 1 = 0, we are able to focus on the diagonal elements [69] σ DC = r d+2z−θ−4…”

mentioning

confidence: 99%

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Sin

Tian

et al. 2018

J. High Energ. Phys.

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“…An interesting generalization of the polynomial model is to consider asymptotically non-relativistic backgrounds which have nontrivial dynamical and hyperscaling violating exponents, z and θ. These kind of solutions are constructed by adding some axion fields to the EMD theories, and has been studied recently in [27] 2 with the following action 3…”

Section: Jhep10(2016)135mentioning

confidence: 99%

Non-local probes in holographic theories with momentum relaxation

Mozaffar

Mollabashi

Omidi

2016

J. High Energ. Phys.

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We consider recently introduced solutions of Einstein gravity with minimally coupled massless scalars. The geometry is homogeneous, isotropic and asymptotically anti de-Sitter while the scalar fields have linear spatial-dependent profiles. The spatiallydependent marginal operators dual to scalar fields cause momentum dissipation in the deformed dual CFT. We study the effect of these marginal deformations on holographic entanglement measures and Wilson loop. We show that the structure of the universal terms of entanglement entropy for d > 2-dim deformed CFTs is corrected depending on the geometry of the entangling regions. In d = 2 case, the universal term is not corrected while momentum relaxation leads to a non-critical correction. We also show that decrease of the correlation length causes: the phase transition of holographic mutual information to happen at smaller separations and the confinement/deconfinement phase transition to take place at smaller critical lengths. The effective potential between point like external objects also gets corrected. We show that the strength of the corresponding force between these objects is an increasing function of the momentum relaxation parameter.

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“…Recently, some of us studied the holographic RG flow for the strongly coupled systems with finite density and disorder [19][20][21], where the charge and energy transport are coupled and the transport coefficients are finite. The partial motivation of the work came from Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In [19][20][21], however, the holographic RG flow was mainly used to study the DC transport on the boundary. In this paper, the first aim is to translate the matrix Riccati equation to the RG flow of AC thermoelectric conductivities, from which one can read the AC thermoelectric conductivities on the boundary.…”

Section: Introductionmentioning

confidence: 99%

Holographic RG flow of thermoelectric transport with momentum dissipation

Wang

et al. 2018

Phys. Rev. D

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We construct the holographic renormalization group (RG) flow of thermoelectric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermoelectric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermoelectric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotropic holographic models which dissipate the momentum and have the finite density, it is found that the RG flow of a particular combination of DC thermoelectric conductivities does not run. As a result, the DC thermal conductivity on the boundary field theory can be derived analytically, without using the conserved thermal current.

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Linear and quadratic in temperature resistivity from holography

Cited by 33 publications

References 90 publications

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Non-local probes in holographic theories with momentum relaxation

Holographic RG flow of thermoelectric transport with momentum dissipation

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