Entangled Dilaton Dyons

Abstract

Einstein-Maxwell theory coupled to a dilaton is known to give rise to extremal solutions with hyperscaling violation. We study the behaviour of these solutions in the presence of a small magnetic field. We find that in a region of parameter space the magnetic field is relevant in the infra-red and completely changes the behaviour of the solution which now flows to an $Ad{S}_2\times R^2$ attractor. As a result there is an extensive ground state entropy and the entanglement entropy of a sufficiently big region on the boundary grows like the volume. In particular, this happens for values of parameters at which the purely electric theory has an entanglement entropy growing with the area, $A$, like $A\log (A)$ which is believed to be a characteristic feature of a Fermi surface. Some other thermodynamic properties are also analysed and a more detailed characterisation of the entanglement entropy is also carried out in the presence of a magnetic field. Other regions of parameter space not described by the $Ad{S}_2\times R^2$ end point are also discussed.

Some comments regarding comparison with weakly coupled Fermi liquid changed, typos corrected and caption of a figure modified

References in corpus (10)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Effective Holographic Theories for low-temperature condensed matter systems
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Holography of Dyonic Dilaton Black Branes
• Entanglement entropy of critical spin liquids
• Fermi surfaces and gauge-gravity duality
• Domain Wall Holography for Finite Temperature Scaling Solutions
• Charged Dilatonic Black Holes and their Transport Properties
• Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes

Cited by in corpus (6)

• Thermal diffusivity and chaos in metals without quasiparticles
• Inhomogeneity simplified
• Intermediate scalings in holographic RG flows and conductivities
• Anisotropic plasmas from axion and dilaton deformations
• Hyperscaling violation : a unified frame for effective holographic theories
• Conductivities from attractors