spontaneous magnetization of quark matter in inhomogeneous chiral phase
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Spontaneous magnetization of quark matter in
inhomogeneous chiral phase
R. YoshiikeCollaborator: K. Nishiyama, T. Tatsumi
(Kyoto University)
QCD phase diagram and chiral symmetry
Various phase structure of quark matter
[K. Fukushima, T. Hatsuda (2011)]
・ Hadronic phase・ Quark-gluon plasma・ Color superconductor etc…
Chiral symmetry
Restored phase0
Current quark mass
SSB Broken phase
0
Constituent quark mass
chiral phase transition line
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)
35352 iiGiLMF
Dual chiral density wave(DCDW) condensate
order parameters: Δ, q
cf. conventional broken phase: .const r
35iz
[G. Basar, et al. (2009)]
Inhomogeneous chiral condensate
35ii r embed the solution of 1+1 dimension
iqzeii 35r
Inhomogeneous chiral phase in QCD phase diagram
Inhomogeneous chiral phase can exist in neutron stars!
T
μ
DCDW phase
Lifshitz point
3.6ρ0 ~ 5.3ρ0
Tri-critical point
restored phase
broken phase
T
μ
2nd
1st
[E. Nakano, T. Tatsumi (2005)]
several ρ0 ~ 10ρ0
・ Homogeneous chiral phase (conventional broken phase) ・・・ Δ≠0, q=0・ DCDW phase ・・・ Δ≠0, q≠0・ Restored phase ・・・ Δ=0 iqze r
Strong magnetic field in neutron stars
Goals・ investigate the magnetic properties of quark matter in DCDW phase・ explain the origin of strong magnetic field in neutron stars
Surface of neutron stars ~ 1012G
(magnetars ~ 1015G)
However, the origin of the magnetic field hasn’t been unraveled.
Phase structure of quark matter in the magnetic fieldThe systems where quark matter can exist in the magnetic field
Neutron stars, Heavy ion collision, Early universe, etc…
T
μB ?
Relevant problem…
Motivation and goals
Thermodynamic potential in the magnetic field
Lagrangian
G
mqziqzmDiLDCDW 4
sincos2
35 )2( Gm
35i
[I. E. Frolov, et al. (2010)]Landau level
1,1,, pnE
2
22
22
222
qpm
nBeq
pm f
(n=1,2, ・・・ ) ・・・ symmetry
(lowest Landau level(LLL), n=0) ・・・ asymmetry
0,,0 BxALandau gauge:
E
0
LLL
asymmetric about zero
2qm
2qm
Thermodynamic potential in the magnetic field
Anomaly by the spectral asymmetryAnomalous baryon number
nomNN
cf. [A. J. Niemi, G. W. Semenoff (1986)]
λk ・・・ eigenvalue of Hamiltonian
In this case
2
1,,
0 2sign
22sign lim
eBq
EEdpeB sLLL
pLLLp
skk
[T. Tatsumi, et al. (2014)]
Regularization on the energy
cf. chiral Lagrangian [D. T. Son, M. A. Stephanov,(2008)]
Thermodynamic potential
2210 ,;,,;,,;,,;,, BemqTBemqTmqTmqBT ff Spectral asymmetry of LLL
Regularizing on the energy, it becomes physically correct.
0 mq-independent
Spontaneous magnetizationStationary condition 2210 ,,,,, eBTmeBTmTmBTm
2210 ,,,,, eBTqeBTqTqBTq
001
0
,;,,,
qmTeB
BTM
B
T=0
m(0)
q(0) M
μ(MeV)μ(MeV)
QM has the spontaneous magnetization in DCDW phase! ~ 1017G
0
,
,;,,
mq
mqBT
2210 eBeB
(MeV) (MeV2)
~ (m(0))2
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
(B=0)
LP(α2=α4=0)
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
(B=0)
LP(α2=α4=0)
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
(B=0)
LP(α2=α4=0)
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
(B=0)
LP(α2=α4=0)
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
① 24
62 8
3
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
2nd order phase transition
Phase boundaries
(B=0)
LP(α2=α4=0)
①
①
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
① 24
62 8
3
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0
LP(α2=α4=0)
(MeV2) (MeV)
2nd order phase transition
②24
62
...1717.0
1st order phase transition
Phase boundaries
(B=0)
LP(α2=α4=0)
②
②
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
① 24
62 8
3
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0 (MeV2) (MeV)
2nd order phase transition
②24
62
...1717.0
1st order phase transition
③ 02
(conventional) 2nd order phase transition
Phase boundaries
(B=0)
③
③
Generalized Ginzburg-Landau expansion
Thermodynamic potential around the Lifshitz point
q
m restored
4
2
homo.
DCDW
4224610
26
4325
2248
24
23
26
220
2
13
9
10
6
13
9
5
4
1
27
5
2
1
qmqmmeBqmqmeB
qmmeBqmeBmeB
eB=0 (MeV2) (MeV) eB=60(MeV)2
~ 1015
G
homo.→ DCDW
m
q
LP(α2=α4=0)
LP(α2=α4=0)
μ-T plane mappingLP(α2=0,α4=0) → LP( )T
μ
m
q
eB=0
m
Switching on B, DCDW region expands andhomogeneous phase changes to DCDW phase!
q
homo.→DCDW
MeVTMeV 130,480
eB=60(MeV)2 ~ 1015 G
(MeV)
MeVT 125
m
q
1st 2ndμ(MeV)
(MeV) 0B
Magnetic properties around Lifshitz point
M
χ
μ(MeV)
0
2
2
B
eB
Magnetic susceptibility does not diverge but has discontinuity
MeVT 125 χ M(MeV2)
0
BeB
M
Spontaneous magnetization Magnetic susceptibility
T
μ
T=125MeV
Ferromagnetic transition point
Summary
• Quark matter in the original DCDW phase has the spontaneous magnetization because 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