1 / 49

San Diego

Beijing. San Diego. Symmetry Restoration and Breaking. Is there a first order phase transition in QCD? Under what conditions will the phase transition and, hence, the chiral symmetry restoration and breaking of center Z(3) symmetry occur?. Finite Density Q C D Phase Transition

tobit
Download Presentation

San Diego

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Beijing San Diego

  2. Symmetry Restoration and Breaking • Is there a first order phase transition in QCD? • Under what conditions will the phase transition and, hence, the chiral symmetry restoration and breaking of center Z(3) symmetry occur?

  3. Finite Density QCD Phase Transition from Lattice Calculation • Finite Density Algorithm with Canonical Approach • Winding Number Expansion Method • Results on NF = 2, and 4 with Wilson Fermion • NF = 3 with Clover Fermion χQCDCollaboration: Anyi Li, Andrei Alexandru, KFL, and XiangfeiMeng PKU, June 29, 2009

  4. Quark Gluon Plasma (QGP) Phase Hardonic Phase

  5. RHIC : Au-Au collisions with 200 GeV/A PHOBOS BRAHMS PHENIX STAR Relativitic Heavy Ion Collider

  6. RHIC Relativistic (ideal) hydrodynamics + initial cond. + freezeout + … Soft physics from lattice QCD -- EoS, Tc etc Hard physics from pQCD -- jet energy loss etc L. Landau (1953) Current Methodology to study QGP T. Hatsuda Lattice ‘06

  7. Phase DiagramUnder Study T Crossover μ We want to study here

  8. Finite density lattice QCD calculations: Multi-parameter Reweighting Taylor Expansion Imaginary Chemical Potential Canonical Ensemble with Reweighting …

  9. Overlap problem

  10. Overlap problem

  11. Canonical partition function

  12. Canonical Ensemble Approach: is real

  13. T T S S A0 A0 T T S S A1 A2

  14. Overlap Problem

  15. Avoid the Overlap Problem KFL (Int. Jou. Mod. Phys. B16, 2017 (2002)) The earlier procedure is like projection after variation (Peierls and Yoccoz) Need variation after projection (Zeh-Rouhaninejad-Yoccoz) Accept/reject based on detB. Unfortunately, this introduces fluctuation problem! Because

  16. Canonical ensembles Discrete Fourier transform Canonical approach K. F. Liu, QCD and Numerical Analysis Vol. III (Springer,New York, 2005),p. 101. Andrei Alexandru, Manfried Faber, Ivan Horva´th,Keh-Fei Liu, PRD 72, 114513 (2005) Standard HMC Accept/Reject Phase Continues Fourier transform Useful for large k WNEM 21 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  17. Instability of discrete Fourier transform It’s difficult to pick up the high frequency modes with discrete Fourier transform Winding number expansion in canonical approach to finite densityXiangfeiMeng - Lattice 2008 Williamsburg

  18. Winding number expansion (I) In QCD Tr log loop loop expansion In particle number space Where Winding number expansion in canonical approach to finite densityXiangfeiMeng - Lattice 2008 Williamsburg

  19. T T S S A0 A0 T T S S A1 A2

  20. Winding number expansion (II) For So The first order of winding number expansion Here the important is that the FT integration of the first order term has analytic solution is Bessel function of the first kind . Winding number expansion in canonical approach to finite density Xiangfei Meng - Lattice 2008 Williamsburg

  21. Winding number expansion test (I) K=12 Winding number expansion in canonical approach to finite density Xiangfei Meng - Lattice 2008 Williamsburg

  22. Winding number expansion test (III) Winding number expansion in canonical approach to finite density Xiangfei Meng - Lattice 2008 Williamsburg

  23. Observables Polyakov loop Baryon chemical potential Phase 29 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  24. Phase Diagrams T T First order ? ρq ρh Mixed phase ρ μ

  25. T plasma hadrons coexistent ρ Phase diagram Two flavors Four flavors ? T plasma hadrons coexistent ρ 31 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  26. Baryon Chemical Potential for Nf = 4 (mπ ~ 1 GeV) 32 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  27. Phase Boundaries from Maxwell Construction Nf = 4 Wilson gauge + fermion action Maxwell construction : determine phase boundary 33 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  28. T plasma hadrons coexistent ρ Phase diagram Two flavors Four flavors ? T plasma hadrons coexistent ρ 35 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  29. Baryon Chemical Potential (mπ ~ 1 GeV) 36 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  30. Three Flavors (Preliminary) mπ ~0.8 GeV

  31. Critical End Point

  32. PolyakovLoop

  33. Quark Condensate

  34. We are here

  35. Summary • Canonical Ensemble Approach overcomes the overlap problem and alleviates the fluctuation problem. No sign problem for T > 0.8 Tc. • Exact algorithm which can discern a first order phase transition from finite volumes. • Wilson fermion on 63 x 4 lattice with mπ ~ 1 GeV shows NF = 2 is 2nd order (?) down to 0.83 Tc, NF = 4 is first order. • Iwasaki + Clover fermion on 63 x 4 lattice with mπ ~ 0.8 GeV results for NF = 3 shows an unambiguous first order phase transition at finite density.

  36. Future • Smaller masses • Larger volume  HNMC (A. Alexandru, et al. arXiv:0711.2678) • Chiral fermion action • Lower temperature (sign problem)

  37. Phase Boundaries Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62 4 flavor (taste) staggered fermion

  38. Polyakov Loop

  39. Winding number expansion (IV) The parameters of Winding number expansion---Fourier series The recursion of Bessel function Winding number expansion in canonical approach to finite density Xiangfei Meng - Lattice 2008 Williamsburg

  40. Phase Boundary (Preliminary) Nf = 4 This work Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62 48 Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

More Related