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Spontaneous magnetization of quark matter in inhomogeneous chiral phase

Spontaneous magnetization of quark matter in inhomogeneous chiral phase. R. Yoshiike Collaborator: K. Nishiyama , T. Tatsumi (Kyoto University). QCD phase diagram and chiral symmetry. Various phase structure of quark matter. c hiral phase transition line. ・ Hadronic phase

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Spontaneous magnetization of quark matter in inhomogeneous chiral phase

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  1. Spontaneous magnetization of quark matter in inhomogeneous chiral phase R. Yoshiike Collaborator: K.Nishiyama, T. Tatsumi (Kyoto University)

  2. QCD phase diagram and chiral symmetry Various phase structure of quark matter chiral phase transition line ・Hadronic phase ・Quark-gluon plasma ・Color superconductor etc… [K. Fukushima, T. Hatsuda(2011)] Chiral symmetry SSB Broken phase Restored phase Constituent quark mass Current quark mass

  3. What’s inhomogeneous chiral phase? “new phase in the high density region of the QCD phase diagram” NJL model in mean field approximation(2-flavor) Inhomogeneous chiral condensate order parameters:Δ, q embed the solution of 1+1 dimension cf. conventional broken phase: Dual chiral density wave(DCDW)condensate z [G. Basar, et al. (2009)]

  4. Inhomogeneous chiral phase in QCD phase diagram T ・Homogeneous chiral phase (conventional broken phase) ・・・Δ≠0, q=0 ・DCDW phase・・・Δ≠0, q≠0 ・Restored phase・・・Δ=0 Lifshitzpoint DCDW phase μ T Tri-critical point 2nd restored phase 1st Inhomogeneous chiral phase can exist in neutron stars! [E. Nakano, T. Tatsumi(2005)] several ρ0～10ρ0 broken phase 3.6ρ0～5.3ρ0 μ

  5. Motivation and goals Strong magnetic field in neutron stars Surface of neutron stars ～1012G T (magnetars～1015G) However, the origin of the magnetic field hasn’t been unraveled. Phase structure of quark matter in the magnetic field μ The systems where quark matter can exist in the magnetic field Neutron stars, Heavy ion collision, Early universe, etc… Relevant problem… B ？ Goals ・investigate the magnetic properties of quark matter in DCDW phase ・explain the origin of strong magnetic field in neutron stars

  6. Thermodynamic potential in the magnetic field Landau level Lagrangian [I. E. Frolov, et al. (2010)] (n=1,2,・・・)・・・symmetry (lowest Landau level(LLL),n=0)・・・asymmetry E 0 Landaugauge: LLL asymmetric about zero

  7. Thermodynamic potential in the magnetic field λk・・・eigenvalue of Hamiltonian Anomaly by the spectral asymmetry Anomalous baryon number cf. [A. J. Niemi, G. W. Semenoff(1986)] In this case cf. chiral Lagrangian [D. T. Son, M. A. Stephanov,(2008)] [T. Tatsumi, et al. (2014)] Regularization on the energy Thermodynamic potential Regularizing on the energy, it becomes physically correct. q-independent Spectral asymmetry of LLL

  8. Spontaneous magnetization Stationary condition (MeV2) (MeV) ～(m(0))2 QM has the spontaneous magnetization in DCDW phase! ～1017G T=0 q(0) M m(0) μ(MeV) μ(MeV)

  9. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) m restored LP (α2=α4=0) DCDW homo. q LP (α2=α4=0)

  10. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) m restored LP (α2=α4=0) DCDW homo. q LP (α2=α4=0)

  11. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) m restored LP (α2=α4=0) DCDW homo. q LP (α2=α4=0)

  12. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) m restored LP (α2=α4=0) DCDW homo. q LP (α2=α4=0)

  13. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) Phase boundaries m ① restored ① LP (α2=α4=0) DCDW 2nd order phase transition homo. q ① LP (α2=α4=0)

  14. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) Phase boundaries m ① restored LP (α2=α4=0) DCDW 2nd order phase transition ② ② homo. 1st order phase transition q LP (α2=α4=0) ②

  15. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point (B=0) eB=0 (MeV2) (MeV) Phase boundaries m ① restored DCDW ③ 2nd order phase transition ② homo. 1st order phase transition ③ q (conventional) 2nd order phase transition ③

  16. Generalized Ginzburg-Landau expansion Thermodynamic potential around the Lifshitz point eB=0 (MeV2) (MeV) eB=60(MeV)2 ～1015Ｇ m m restored LP (α2=α4=0) DCDW homo. q q LP (α2=α4=0) homo.→ＤＣＤＷ

  17. μ-T plane mapping LP(α2=0,α4=0)　→　LP() (MeV) T m m (MeV) μ eB=0 eB=60(MeV)2～1015Ｇ q m q q μ(MeV) 2nd 1st homo.→DCDW Switching on B, DCDWregion expands and homogeneous phase changes to DCDW phase!

  18. Magnetic properties around Lifshitz point Magnetic susceptibility Spontaneous magnetization T χ M(MeV2) χ μ M T=125MeV μ(MeV) Ferromagnetic transition point Magnetic susceptibility does not diverge but has discontinuity

  19. Summary • Quark matter in the original DCDW phase has the spontaneous magnetizationbecause of spectral asymmetry. • Magnetic susceptibility has discontinuity on the phase transition point. • Magnetic field spreads DCDW phase and changes homogeneous phase to DCDW phase. Future work • We want self-consistent conclusion taken account for magnetic field by the spontaneous magnetization. Neutron stars

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