Spontaneous momentum dissipation and coexistence of phases in holographic Horndeski theory

Abstract

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.

A unified description of translational symmetry breaking in holography

“…See[32,34,35,[53][54][55][56][57][58] for other studies of the interplay of spontaneous and explicit breaking of translations in holography and field theory.…”

Hairy Taub-NUT/Bolt-AdS solutions in Horndeski theory

“…Its space of solutions is endowed with hairy black holes [78][79][80][81][82], boson stars [83], and neutron stars with polytropic and realistic equations of state with and without rotation [84,85]. In the context of holography, different aspects of this theory have been explored, for instance, asymptotically Lifshitz black holes with fractional critical exponent [86], holographic entanglement entropy [87], and models with spontaneous momentum dissipation [88][89][90][91][92][93], among others [94,95]. Recently, holographic heat engines were analyzed in Ref.…”

A simple holographic model for spontaneous breaking of translational symmetry

“…Holographic duality provides a tractable approach to the physics of strong correlated systems by mapping the many-body problems to classical gravity problems. Recently, some holographic effective models for solid states that spontaneously break the translations have been constructed [5][6][7][8][9][10][11][12][13][14]. A common feature in these models is that the translations are spontaneously broken in a homogenous manner(For inhomogeneous realizations, one can refer to [15][16][17][18][19][20][21][22]).…”