### Speaker

Kazuya Nishiyama
(Kyoto U.)

### Description

There have been theoretically and experimentally explored the QCD phase diagram in the density ($\mu$)-temperature ($T$) plane.
Usually the phase structure is studied by assuming the spatially and temporally constant order parameter.
Recently the possibility of inhomogeneous chiral phase has attracted much interest [1,2] in the light of progress in heavy-ion collisions or observation of compact stars. Theoretically discovering of the Hartree-Fock solutions in 1+1 dimension has also stimulated the studies.
The effect of the external magnetic field on the chiral transition or deconfinement has been also studied by the lattice QCD simulation for $\mu=0$ [3].
It should be important, because quark matter is exposed in the strong magnetic field in compact stars or heavy-ion collisions. Theoretically the magnetic field leads to various
phenomena in QCD such as chiral magnetic effect, magnetic catalysis or magnetic
inhibition of the spontaneous symmetry breaking effect.
We study the chiral transition in the presence of the magnetic field by using the
NJL model. We focus here on the inhomogeneous chiral phase. For the analysis, the complex order parameter $\Delta := -2G\left[ \left<\overline \psi \psi \right> +i\left<\overline \psi i\gamma^5\tau^3\psi \right>\right]$ is used; dual chiral
density wave (DCDW) $\left[ \Delta(x) =me^{iqz} \right]$ and real kink crystal (RKC) $\left[ \Delta(x) =\frac{2m\nu}{1+\sqrt{\nu}}{\rm sn}\left( \frac{2mz}{1+\sqrt{\nu}}, \nu\right) \right]$ have been commonly used
as typical configurations. The properties of DCDW has been studied by Frolov et al.
in the presence of the magnetic field [4]. They found that DCDW phase develops in a wide
density region at $T=0$. They also found some peculiar behavior of the amplitude
and the wavevector. However, they did not take into account the possibility of RKC,
while RKC has been suggested to be favored in the absence of the magnetic field.
Here we introduce the hybrid configuration $
\left[ \Delta(x) = \frac{2m\nu}{1+\sqrt{\nu}}{\rm sn}\left( \frac{2mz}{1+\sqrt{\nu}},\nu \right)e^{iqz} \right]
$, which smoothly connects both DCDW
and RKC, and demonstrate that the magnetic field favors the phase modulation: it is
found through the analysis of the thermodynamic potential that the wavevector $q$
takes a nonzero value in the presence of the magnetic field and DCDW and RKC
coexist in the weak magnetic field at moderate densities. In the high magnetic field
pure DCDW appears over all density region. It is also shown that there is a first order phase transition between inhomogeneous phases in the presence of magnetic field.
Such hybrid phase may appear in compact stars.
[1] E.Nakano, T.Tatsumi, Phys.Rev.D 71 (2005) 114006
[2] D.Nickel, Phys.Rev.D 80 (2009) 074025; D.Nickel, Phys.Rev.Lett.103 (2009) 072301
[3] GH.S.Bali, F.Bruckmann, G.Endrodi, Z.Fodor, S.D.Katz, A.Schafer, Phys. Rev.D86 (2012) 071502
[4] I.E.Frolov, V.Ch.Zhukovsky, K.G.Klimenko, Phys. Rev. D82 (2010) 076002

### Primary author

Kazuya Nishiyama
(Kyoto U.)

### Co-authors

Shintaro Karasawa
(Kyoto U.)
Toshitaka Tatsumi
(Kyoto U.)