Ginzburg–Landau Phase Diagram under Magnetic Field

Abstract

We study the modification of the chiral phase structure of QCD due to an external magnetic field within a generalized Ginzburg-Landau framework. In the chiral limit, the effect is found to be so drastic that it brings a "continent" of chiral spiral in the phase diagram, by which the chiral tricritical point is totally washed out. The current quark mass protects the chiral critical point from a weak magnetic field. However, the critical point is eventually to be covered by the chiral spiral phase as the magnetic field grows. KEYWORDS: QCD phase diagram, Inhomogeneous phase, Chiral symmetry, Magnetic fieldIntroduction, Methods, and Results. There has recently been a growing interest on possible crystal structures in the chiral condensate in QCD at finite density [1]. On the other hand, the effect of magnetic field on QCD has also been the subject of intensive studies. Phenomenologically, exploring possible forms of strongly interacting matter under the magnetic field is relevant to the physics of magnetars; the compact stellar objects known to have a strong magnetic field, B ∼ 10 10 T.We here report our recent study of the effect of strong magnetic fields on the inhomogeneous chiral phase structure [2]. Several studies are already devoted on how the magnetic field affects the critical points and phase structures [3][4][5][6]. The effect of current quark mass on a particular type of inhomogeneous chiral condensate is also studied in [7].We focus on the neighborhood of the critical point. We first show that in this case it is possible to derive systematically the generalized Ginzburg-Landau (gGL) action without specifying the spatial form of the chiral condensate. We derive this functional up to the first nontrivial order in the current quark mass h and the magnetic field B. It turns out that these two ingredients bring competing effects on inhomogeneous phases. In particular, the condensate accompanied by the complex phase, the chiral spiral, is found to be favored by the magnetic field [6], and accordingly the phase diagram is to be drastically changed once the effect of magnetic field prevails.The gGL action density at the first nontrivial order in the external magnetic field B and the current quark mass m q can be derived in the same way as described in [8,9]. Up to the sixth order in the scalar and pseudoscalar condensates, σ and π a (a = 1, 2, 3), as well as in ∇ ≡ ∂ x , the result is [2]

Magnetic field effect on nuclear matter from a Skyrmion crystal model

“…5. Similar observations, regarding the deformation of inhomogeneities for the chiral condensate by magnetic effects, have been made in different models [18][19][20][21].…”

“…Interestingly enough, 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 almost intact. (Similar observations, regarding the deformation of inhomogeneities for the chiral condensate by magnetic effects, have been made in different models [18][19][20][21]. )…”

Chiral-imbalance density wave in baryonic matters

“…The emergence of this chiral-imbalance density wave would significantly contribute to studies on the chiral phase transition under a magnetic field with the inhomogeneous chiral condensates (chiral density waves) incorporated, as has been discussed in [41][42][43] in different setup for chiral effective models, and also on the nuclear matter structure, in compact stars holding a magnetic field.…”

“…Now, consider a high-dense matter system under a magnetic field, inside of which charged pions form the pion-vector current J π µ = i(∂ µ π + π − − π + ∂ µ π − ), 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.…”