Solitonic modulation and Lifshitz point in an external magnetic field within Nambu--Jona-Lasinio model

TL;DR

This paper investigates how an external magnetic field influences inhomogeneous solitonic chiral condensates and the Lifshitz point within the Nambu--Jona-Lasinio model, revealing oscillatory behaviors akin to de Haas-van Alphen effects.

Contribution

It introduces a new Ginzburg-Landau expansion method to efficiently determine chiral restoration lines and explores the magnetic field's impact on the Lifshitz point in the phase diagram.

Findings

Both boundaries of solitonic modulation oscillate with magnetic field (dHvA oscillations).

The Lifshitz point's temperature increases monotonically with magnetic field.

Oscillations are observed in phase diagram boundaries and Lifshitz point locations.

Abstract

We study the inhomogeneous solitonic modulation of a chiral condensate within the effective Nambu--Jona-Lasinio model when a constant external magnetic field is present. The self-consistent Pauli-Villars regularization scheme is adopted to manipulate the ultraviolet divergence encountered in the thermodynamic quantities. In order to determine the chiral restoration lines efficiently, a new kind of Ginzburg-Landau expansion approach is proposed here. At zero temperature, we find that both the upper and lower boundaries of the solitonic modulation oscillate with the magnetic field in the $\mu$--$B$ phase diagram which is actually the de Hass-van Alphan (dHvA) oscillation. It is very interesting to find out how the tricritical Lifshitz point $(T_L,\mu_L)$ evolves with the magnetic field: There are also dHvA oscillations in the $T_L$--$B$ and $\mu_L$--$B$ curves, though the tricritical temperature $T_L$ increases monotonically with the magnetic field.