Entangled Dilaton Dyons

TL;DR

This work analyzes a 3+1 dimensional Einstein-Maxwell-Dilaton gravity model with hyperscaling-violating electric solutions to understand how a small magnetic field reshapes infrared physics. The authors show that for parameter regions with $|\\alpha|>|\\delta|$, the magnetic field becomes IR relevant and drives the flow to an $AdS_2\times R^2$ attractor, yielding extensive ground-state entropy and volume-like entanglement for large boundary regions, in contrast to the $S_{EE}\sim A\log A$ behavior seen in the purely electric case near certain lines such as $\alpha=-3\delta$. They classify the IR outcomes into three cases based on the relation between $\alpha$ and $\delta$, derive thermodynamic properties including a linear-in-temperature specific heat and a diamagnetic magnetization, and study how a small $Q_m$ alters the entanglement entropy across scales, including a crossover scale $L_*$ that signals a transition to the magnetic IR regime. The results illuminate a gravity mechanism for Fermi-surface-like entanglement and illustrate how magnetic perturbations can qualitatively modify IR physics while preserving compressibility, offering insights for holographic descriptions of non-Fermi liquids and guiding future string-theory embeddings. Overall, the paper connects hyperscaling violation, IR attractors, and entanglement structure in a unified holographic framework with clear thermodynamic and entanglement signatures.

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.

Figures (8)

• Figure 1: The blue and green shaded regions are allowed by the various positivity and thermodynamics constraints for the electric scaling solutions. The straight lines in the $(\delta,\alpha)$ plane demarcate various regions which will be relevant for the discussion in the following sections.
• Figure 2: Figure showing various region in $(\delta,\alpha)$ space. Details of these regions can be found in Table (1)
• Figure 3: Different contributions to $V_{eff}$ in Log-Log plot. Blue$\rightarrow$ Scalar Potential $b^4(r) {e^{2\delta \phi}\over 2}$, Black$\rightarrow$$Q_e^2 e^{-2\alpha \phi}$ term, Red$\rightarrow$$Q_m^2 e^{2\alpha \phi}$ term.
• Figure 4: In the top plot, $a(r) \sim r^{\gamma}$ with $\gamma_{Fit}=0.706$ whereas $\gamma_{Analytical}=0.707$. In the bottom plot, $b(r) \sim r^{\beta}$ with $\beta_{Fit}=0.391$ whereas $\beta_{Analytical}=0.390$.
• Figure 5: $\phi=k \ log[r]$. $k_{Fit}= -0.4858$ as compared to $k_{Analytical}=-0.4878$.