Exploring Anisotropic Effects in Magnetized Quark Matter

TL;DR

This work probes how strong magnetic fields induce pressure anisotropy and rich Landau-level dynamics in cold, dense quark matter using a covariant nonlocal NJL model. By solving the mean-field, gauge-invariant framework and employing a Landau-level formalism with a regularized grand potential, the authors extract $P_{\parallel}$, $P_{\perp}$, $n$, $\varepsilon$, $\mathcal{M}$, $\chi_M$, and $C_{s,\parallel}$, $C_{s,\perp}$ across varying $\mu$ and $eB$, comparing the chiral limit to finite current masses. They find a robust anisotropy: $P_{\parallel}$ stiffens and approaches the causal bound in the LLL limit, while $P_{\perp}$ is suppressed, and the system exhibits de Haas–van Alphen–like oscillations in magnetization and susceptibility tied to Landau-level filling; finite quark masses preserve the qualitative picture but soften level transitions, with $\mu$IMC emerging at finite $\mu$ and strong fields. The results persist across mass regimes and agree qualitatively with local NJL studies, offering a solid baseline for future finite-temperature and $\beta$-equilibrium explorations and lattice comparisons.

Abstract

We investigate the thermodynamic properties of cold magnetized quark matter within a nonlocal Nambu Jona Lasinio (nlNJL) model. Our study addresses the equation of state, anisotropic pressures, quark density, speed of sound, and magnetic susceptibility, with direct comparison to the chiral limit. Strong magnetic fields are found to generate marked anisotropy: the longitudinal pressure and speed of sound are enhanced, approaching the causal bound in the lowest Landau-level (LLL) regime, while the transverse components are systematically reduced. The quark density exhibits magnetic catalysis, increasing with both the chemical potential and the magnetic field strength. At moderate to high fields, the critical chemical potential decreases with increasing $eB$, signaling the occurrence of inverse magnetic catalysis at finite chemical potential ($μ$IMC). Magnetic susceptibility displays oscillations around zero in low fields, driven by de Haas van Alphen like effects, and settles at positive values for strong fields, consistent with an overall growth of magnetization. Compared with the chiral limit, the inclusion of finite current quark masses does not modify the overall oscillatory behavior, but changes the nature of the Landau level transitions, which become weakly first order instead of second order.

Figures (11)

• Figure 1: Normalized longitudinal ($P_{\parallel}$) and transverse ($P_{\perp}$) pressures as functions of the magnetic field strength $eB$ and the quark chemical potential $\mu$ in the chiral limit. In all cases, dashed curves correspond to the $\chi SB$ phase and solid curves to the $\chi SR$ phase and the first-order chiral phase transition is marked by a dot.
• Figure 2: Quark number density $n$ as a function of (a) the magnetic field $eB$ and (b) the quark chemical potential $\mu$. Results are shown for three representative chemical potentials, as indicated in (a) and several magnetic field strengths in (b).
• Figure 3: Normalized magnetization as function of (a) the magnetic field $eB$ and (b) the quark chemical potential $\mu$, for the chiral limit.
• Figure 4: Magnetic susceptibility as function of magnetic field $eB$ for different values of quark chemical potential $\mu$, within the chiral limit.
• Figure 5: Normalized longitudinal (solid) and transverse (dashed) pressures (a)-(c) and corresponding squared sound velocities $c_s^2$ (d)-(f) as functions of the dimensionless energy density $\varepsilon/\varepsilon_c$. Results are shown for three magnetic field strengths: $eB=0.05$ GeV$^2$ ((d), $\varepsilon_c=184.1$ MeV/fm$^3$), $eB=0.3$ GeV$^2$ ((e), $\varepsilon_c=313.7$ MeV/fm$^3$), and $eB=0.5$ GeV$^2$ ((f), $\varepsilon_c=672.0$ MeV/fm$^3$).