Phases of planar AdS black holes with axionic charge

Caldarelli, Marco M.; Christodoulou, Ariana; Papadimitriou, Ioannis; Skenderis, Kostas

doi:10.1007/jhep04(2017)001

Cited by 64 publications

(78 citation statements)

References 64 publications

(157 reference statements)

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“…Unlike the previous studies, we first study D ± at finite density without any approximation and deduce the property of D c and D e in the incoherent regime. We consider two holographic models: the linear axion model [27] and one of the axion-dilaton models [28,29] based on the Gubser-Rocha model [30]. We choose these models because both allow the analytic solutions and they are related in the sense that at zero density the axion-dilaton model undergoes the phase transition to the linear axion model if the momentum relaxation is weak.…”

Section: Jhep06(2017)030mentioning

confidence: 99%

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Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

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Abstract:We study diffusion and butterfly velocity (v B ) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (µ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D ± describing the coupled diffusion of charge and energy. By computing D ± exactly, we find that in the incoherent regime (β/T 1, β/µ 1) D + is identified with the charge diffusion constant (D c ) and D − is identified with the energy diffusion constant (D e ). In the coherent regime, at very small density, D ± are 'maximally' mixed in the sense that D + (D − ) is identified with D e (D c ), which is opposite to the case in the incoherent regime. In the incoherent regime D e ∼ C − v 2 B /k B T where C − = 1/2 or 1 so it is universal independently of β and µ. However, D c ∼ C + v 2 B /k B T where C + = 1 or β 2 /16π 2 T 2 so, in general, C + may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

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Section: Jhep06(2017)030mentioning

confidence: 99%

“…To determine which one corresponds to the ground state solution, we compare the grand potential density of two solutions. The grand potential density (G) is the on-shell action divided by the spatial volume and temperature [29] …”

Section: Jhep06(2017)030mentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

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“…Then the dual system may be interpreted as some kind of "electronic crystals", whose impacts on the transport or elastic properties are also worth studying. In [38,39], a general framework has been developed for computing the holographic 2-point function and the corresponding conductivities dual to a broad class of Einstein-Maxwell-Axion-Dilaton theories. We can generalize this study to include the higher derivative axion terms and see what novel phenomena emerge.…”

Section: Discussionmentioning

confidence: 99%

A simple holographic model for spontaneous breaking of translational symmetry

2019

Eur. Phys. J. C

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It has been shown that holographic massive gravities can effectively realize spontaneous breaking of translational symmetry in homogenous manners. In this work, we consider a toy model of such category by adding a special gauge-axion coupling to the bulk action. Firstly, we identify the existence of spontaneous breaking of translations by the analysis on the UV expansion. In the absence of explicit breaking, the black hole solution is simply the same as the Reissner-Nodström(RN) black holes, regardless of the non-trivial profile of the bulk axions. The associated Goldstone modes exist only when the charge density is non-zero. Then, we investigate the optical conductivity both analytically as well as numercially. Our result perfectly agrees with that for a clean system, while the incoherent conductivity gets modified due to the symmetry breaking. The transverse Goldstone modes are dispersionless since the solution is dual to a liquid state. Finally, the effect of momentum relaxation to the transverse modes is considered. In this case, the would-be massless modes are pinned at certain frequency, which is another key difference from the unbroken states.

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“…The boundary conditions that the solution satisfies is determined by demanding that the solution is regular. This in turn determines what is the boundary condition that the hairy black holes are compatible with [68,69]. A discussion about the boundary conditions for computing the mass of hairy black holes that preserve the asymptotic anti-de Sitter invariance is given in [70].…”

Section: B Thermodynamicsmentioning

confidence: 99%

Spontaneous momentum dissipation and coexistence of phases in holographic Horndeski theory

et al. 2019

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We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory. In the probe limit breaking the translational invariance, we study the conductivity and we find a non-trivial structure indicating a collective excitation of the charge carriers as a competing effect of momentum dissipation and the coupling of the scalar field to Einstein tensor. Going beyond the probe limit, we investigate the spontaneous breaking of translational invariance near the critical temperature and discuss the stability of the theory. We consider the backreaction of the charged scalar field to the metric and we construct numerically the hairy black hole solution. To determine the dual phases of a hairy black hole, we compute the conductivity. When the wave number of the scalar field is zero, the DC conductivity is divergent due to the conservation of translational invariance. For nonzero wave parameter with finite DC conductivity, we find two phases in the dual theory. For low temperatures and for positive couplings, as the temperature is lower, the DC conductivity increases therefore the dual theory is in metal phase, while if the coupling is negative we have the opposite behavior and it is dual to an insulating phase. We argue that this behavior of the coupling of the scalar field to Einstein tensor can be attributed to its role as an impurity parameter in the dual theory.

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Phases of planar AdS black holes with axionic charge

Cited by 64 publications

References 64 publications

Diffusion and butterfly velocity at finite density

Diffusion and butterfly velocity at finite density

A simple holographic model for spontaneous breaking of translational symmetry

Spontaneous momentum dissipation and coexistence of phases in holographic Horndeski theory

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