Phase structure of SCL-QCD with baryon and isospin density

1. Phase structure of SCL-QCD with baryon and isospin density Phys.Rev.D69, 094501 (2004) Introduction -- finite density QCD -- Formulation of SCL-QCD Phase structures in T-mB plane Phase structures in T-mI plane Summary Yusuke Nishida(Univ. of Tokyo) Chiral05@RIKEN 15/Feb/05

2. Introduction • QCD phase diagram in T-m plane from HP of M. Alford Finite density QCD • Neutron superfluidity • Pion/Kaon condensation • Color superconductivity Complex fermion determinant in Monte-Carlo lattice simulations

3. Strong coupling lattice QCD • 3-color QCD with baryon/isospin density • physical interpretation of phase structures • analytical formulae for phase transitions QCD Lagrangian Effective action analytic! 3-color : Damgaard, Hochberg and Kawamoto (1985) Bilic, Demeterfi and Petersson (1992) 2-color :Dagotto, Karsch and Moreo (1986) • Dagotto, Moreo and Wolff (1987) • Qualitative agreement with MC lattice simulations in 2-color QCD with baryon density Yusuke Nishida et al., Phys.Rept.398, 281 (2004)

4. Formulation • KS lattice action with m Hasenfratz and Karsch,PLB125, 308 (1983) 2 species of KS fermion ～ Nf=4×2 continuum flavors

5. How to derive effective action Damgaard et al, PRL53,2211 (1984) • Strong coupling limit : • 1/d expansion and integration over • Bosonization of with : • Mean field approximation : • Exact integration over , and • Effective action with p=0

6. Phase diagram in T-mB plane • Nc=3, Nf=8, mI=0 • Existence of TCP → CEP (m=0) • Positive gradient at TCP • Nf↑⇒Tc↓ / Nf=4 m Increasing thermal excitations m=0 m=0.4

7. Effect of small mI • mI=0.2, m=0.4 • 1st order line splits • Tc increases mI=0 <su> <sd> mI mI

8. Effective action with mI • Effective action at mB=0 • Pion condensate g→∞, 1/d expansion, MFA Exact integration over , and

9. Condensates vs. mI • T=0m=0.02 Maximum density mI Continuum rotation from sto p Saturation effect rIvs. p

10. What is saturation? Full density Isospin current=0 Condensate=0 Hopping p p p p Analogous phenomenon with Mott insulator cf. Hardcore boson Hubbard model : PRL88, 167208

11. mI mI Kogut & Sinclair, PRD66, 034505 (2002) Lattice data • T=0, m=0.025 m=0.02, Nf=8, b=0 p s Qualitative agreement with our results Saturation effect occurs at mI~2

12. 3D phase diagram • (T,mI,m)-space Pioncondensationphase All phasetransitionsare2nd order Saturatedsystem Vacuum

13. Summary • Phase structure in T-mB • Positive gradient at TCP • Phase structure in T-mI • Continuum rotation from sto p • p=0 with saturation ⇒ analogy to MI • Agreement with MC sim. • Future problem • s &pin T-mB-mI • CSC (qq) • Nf↑⇒ Tc↓ m=0 T s=0 / TCP mB p=0 / mI

14. Backup slides

15. 1/d expansion • integration Higher order terms contain more quark fields = more 1/d

16. Density / entropy jump • T=0.8, m=0 • Generalized Clapeyron-Clausius relation Nf=4 <Halasz et al., PRD58, 096007 (1998)> Positive gradientnear TCP/CEP

17. Density / entropy jump • Leading order of 1/d expansion • integration • Entropy of static baryons baryonic mesonic Baryons are static!

18. 3-color QCD with mI Chiral symmetry at m=mI=0 NG boson : pion Pion condensation for mI>mp 2-color QCD with mB Pauli-Gursey sym. at m=mB=0 NG boson : diquark Diquark cond. for mB>mD 3c-QCD(mI) vs. 2c-QCD(mB) ..

19. 3D phase diagram • (T,mI,m)-space M.I. M.I. cf. Hardcore bosonHubbard model at T=0 PRL 88, 167208 (2002) Saturatedsystem Vacuum Pion superfluid