Magnetic field effect on nuclear matter from a Skyrmion crystal model

Abstract

We explore magnetic field effects on the nuclear matter based on the skrymion crystal approach for the first time. It is found that the magnetic effect plays the role of a catalyzer for the topological phase transition (topological deformation for the skyrmion crystal configuration from the skrymion phase to half-skyrmion phase). Furthermore, we observe that in the presence of the magnetic field, the inhomogeneous chiral condensate persists both in the skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic field gets larger, the inhomogeneous chiral condensate in the skyrmion phase tends to be drastically localized, while in the half-skyrmion phase the inhomogeneity configuration is hardly affected. It also turns out that a large magnetic effect in a low density region distorts the baryon shape to an elliptic form but the crystal structure is intact. However, in a high density region, the crystal structure is strongly effected by the strong magnetic field. A possible correlation between the chiral inhomogeneity and the deformation of the skrymion configuration is also addressed. The results obtained in this paper might be realized in the deep interior of compact stars.

Chiral-imbalance density wave in baryonic matters

“…It is dobbed "chiral-imbalance density wave". We also observe that the periodicity of the chiral-imbalance density wave harmonizes to almost coincide with the previously proposed inhomogeneouschiral condensate distributions induced on the skyrmion crystal [44].…”

“…• As the strength of a magnetic field increases, the inhomogeneity of φ 1 tend to be localized and the amplitude of φ 1 becomes small, as discussed in [44].…”

“…• In contrast to the skyrmion phase, the magnetic effect is insensitive to the inhomogeneous configuration of φ 1 , as discussed in [44].…”

“…), coupled to the electromagnetic field, and then might also couple to the electromagnetic U (1) A anomaly as above. Of importance here is to note that as discussed in [41][42][43][44], in a high-dense medium with a strong magnetic field, the pions can locally form condensates, (so-called inhomogeneous chiral condensates), so that the pion-vector current J π µ can also have a locally nontrivial distribution in the medium. Suppose the medium to be so high-dense like that, in such a way that the dense matter can be highly compressed to be almost static.…”

“…crystal approach, the baryonic matter can also be described as the topologically static-object. In high density region, where baryons is so compressed to be a static object, the skyrmion crystal is a powerful approach for the qualitative-baryon description #2 as if they could form crystals [44,[53][54][55][56][57][58][59][60][61].…”