Holographic Magnetic Phase Transition

TL;DR

The paper investigates four-dimensional interacting fermions in a strong magnetic field within the holographic Sakai-Sugimoto model, focusing on the deconfined, chiral-symmetric parallel phase. Using the D8-brane DBI+CS action, it reveals a two-component charge structure—horizon charge and smeared D4-brane (baryon-like) charge—whose redistribution as the magnetic field is varied triggers a first-order phase transition with a jump in magnetization, consistent with a transition toward the lowest Landau level. Analytic control is achieved at zero temperature, where the transition occurs at $h \approx 0.19$ and the high-field regime satisfies $\mu = \frac{d}{3h}$ and $F = \frac{d^2}{6h}$ with all charge carried by boundary-proximate smeared D4-branes; finite temperature introduces a critical line $T_c(d)$ ending at a critical point, after which the transition smooths to a cross-over. The work connects the holographic description to lowest-Landau-level physics and predicts anomaly-driven currents and distinct transport signatures across the transition, offering qualitative insights into strongly coupled fermions in magnetic fields and potential parallels with metamagnetism and related phenomena.

Abstract

We study four-dimensional interacting fermions in a strong magnetic field, using the holographic Sakai-Sugimoto model of intersecting D4 and D8 branes in the deconfined, chiral-symmetric parallel phase. We find that as the magnetic field is varied, while staying in the parallel phase, the fermions exhibit a first-order phase transition in which their magnetization jumps discontinuously. Properties of this transition are consistent with a picture in which some of the fermions jump to the lowest Landau level. Similarities to known magnetic phase transitions are discussed.

Figures (6)

• Figure 1: A plot showing the three solutions to the integral equation (\ref{['zintegralequation']}) for $z_{\infty}$ with $d=1$ and regulator $\epsilon = 10^{-3}$. The dashed red curve is $z_{\infty}$ while the solid blue curve is the regulated integral on the right hand side of (\ref{['zintegralequation']}). The values of $z_{\infty}$ at which the curves cross are solutions. The regulator is responsible for the plateau in the integral; as $\epsilon$ is decreased, the plateau is pushed higher, and when $\epsilon \to 0$ the largest solution is $z_{\infty} = \infty$.
• Figure 2: Three solutions for (a) the free energy $F$ and (b) the magnetization $M$ at $T=0$ with $d =1$. There is a first-order phase transition from the solid blue $z_\infty \sim h$ solution to the dashed red $z_\infty \to \infty$ solution at $h = 0.19$. The dotted grey solution, which corresponds to the middle solution in Fig. \ref{['zinfinity_fig']}, connects the two stable solutions and is an unstable maximum of the free energy.
• Figure 3: (a) Three solutions for $A_1(\infty)$ as a function of $A_1(u_T)$ for $n=1$, $T=0.07$, and $h =0.2$. (b) The free energy $F$ as a function of $h$ for $n=1$ and $T=0.09$. There are two stable branches, the solid blue curve and the dashed red curve. The phase transition, where the blue and red curves cross, is at $h=0.235$.
• Figure 4: (a) $\mu$ and (b) $M$ are smooth functions of $h$ for $d=1$ and $T=0.102$ which is just above the critical point at $T=0.101$.
• Figure 5: (a) $\mu$ and (b) $M$ as functions of $h$ for $d=1$ and $T=0.09$, below the critical point. There are now two branches of stable solutions, and the phase transition between them occurs at $h = 0.235$.