Yusuke Nishida (U. Tokyo) hep-ph/0312371

1
Phase structures of strong coupling lattice QCD
with finite baryon and isospin density

• Yusuke Nishida (U. Tokyo) hep-ph/0312371

• Finite density QCD e.g. neutron star interiors
• Monte-Carlo lattice simulations
• Complex fermion determinant
• Small lattice volume or low mB high T

Fodor Katz (2002), Forcrand Philipsen
(2002), Allton et al. (2002), DElia Lombardo
(2003),
2
Strong coupling lattice QCD

• QCD Lagrangian Effective action
• analytic !
• Qualitative success in 2-color QCD
• 3-color QCD with baryon and/or isospin density

D
m
Kogut et al., NPB642, 181
Y.N. et al., hep-ph/0306066
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Formulation

• Lattice action with 2 KS fermions
• Effective action with
• Non-trivial coupling between
• up and down due to integration

Nf42 continuum flavors
g?8, 1/d expansion, MFA
Exact integration over , and
4
Phase diagram in T-mB plane

• Nc3, Nf8, mI0

• Existence of TCP
• ? CEP (m0)
• Positive gradient at TCP
• Nf??Tc?

/
Nf4
Increasing thermal excitations
m0
m0.4
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Pion condensation with mI

• 3-color QCD with mI
• Chiral symmetry at mmI0
• NG boson pion
• Pion condensation for mI gt mp

• 2-color QCD with mB
• Pauli-Gursey sym. at mmB0
• NG boson diquark
• Diquark cond. for mB gt mp

..
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Condensates vs. mI

• T0m0.02

(2-color with mB)
mI
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Lattice data
Kogut Sinclair, PRD 66, 034505 (2002)

• T0, m0.025

Pion condensate
Chiral condensate
mI
mI
Qualitative agreement with our results
Saturation effect occurs at mI 2
8
What is saturation ?
Full density Isospin current 0 Condensate
0
Hopping
p
p
p
p
Analogous phenomenon with Mott insulator
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3D phase diagram

• ( T , mI , m ) - space

Pioncondensationphase
All the phasetransitions are2nd order
Saturatedsystem
Vacuum
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Summary

• Phase structure in T-mB
• Positive gradient at TCP
• Phase structure in T-mI
• 3c-QCD(mI) ? 2c-QCD(mB)
• Agreement with MC sim.
• p0 with saturation
• ? MI phenomena
• Future problem
• Phase structure
• in T-mB-mI

• Nf?? Tc?

m0
T
s 0
/
TCP
mB
p0
/
mI