Entangled Dilaton Dyons

TL;DR

This paper investigates how a small magnetic field influences extremal Einstein-Maxwell-dilaton solutions, revealing a transition to an $AdS_2\times R^2$ attractor with extensive entropy and volume-law entanglement, contrasting purely electric cases.

Contribution

It demonstrates that a magnetic field can dominate IR behavior in Einstein-Maxwell-dilaton solutions, leading to new attractor geometries and entanglement properties not seen in purely electric scenarios.

Findings

Magnetic field induces an $AdS_2\times R^2$ IR attractor.

Ground state entropy becomes extensive with magnetic field.

Entanglement entropy can grow with volume under magnetic influence.

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 $AdS_2\times R^2$ 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 $AdS_2\times R^2$ end point are also discussed.