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Lattice QCD at Non-Zero Temperature and Density with Wilson and Neuberger Quarks

Lattice QCD at Non-Zero Temperature and Density with Wilson and Neuberger Quarks. Xiang-Qian Luo (with H.S. Chen, L.K. Wu, X.L. Yu) Zhongshan University, Guangzhou, China. Outline. Introduction Lattice Formulation First Results from lattice QCD with Wilson and Neuberger Quarks Conclusion.

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Lattice QCD at Non-Zero Temperature and Density with Wilson and Neuberger Quarks

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  1. Lattice QCD at Non-Zero Temperature and Density with Wilson and Neuberger Quarks Xiang-Qian Luo (with H.S. Chen, L.K. Wu, X.L. Yu) Zhongshan University, Guangzhou, China

  2. Outline • Introduction • Lattice Formulation • First Results from lattice QCD with Wilson and Neuberger Quarks • Conclusion X.Q. Luo

  3. I. Introduction According to the big bang model in cosmology, the early universe underwent a series of drastic changes. For some time it was a hot and dense quark-gluon plasma (QGP), where quarks and gluons were deconfined. Today it is in a low temperature and low density hadronic phase, where quarks are confined. X.Q. Luo

  4. The ultimate goal of machines such as • RHIC (Relativistic Heavy Ion Collider) • LHC (Large Hadron Collider) is to create the QGP phase, and replay the birth and evolution of the Universe. X.Q. Luo

  5. Phase diagram of QCD at zero-density Satz’s and Aoki’s talks X.Q. Luo

  6. QCD Phase Diagram Four fermion model: Alford, Wilczek, et al., X.Q. Luo

  7. Plenary talks at this conference • June 18 Morning; Heavy-Ion & QCD Phases8:30-9:05 H. Satz, Bielefeld Critical Behavior in QCD (35')9:05-9:40 S. Aoki, University of Tsukuba QCD Phases in Lattice QCD (35')9:40-10:15 T. Hatsuda, University of TokyoSignatures of Deconfinement and Chiral-Symmetry Restoration (35') 10:35-11:10 X. N. Wang, Lawrence Berkeley National Lab Probing the Strongly Interacting Quark-Gluon Plasma via Jet Quenching (35')11:10-11:45 L. Mclarren, Brookhaven National Lab RHIC and New Forms of Matter (35')11:45-12:20 J. W. Qiu, Iowa State University QCD Quantum Coherence in High-Energy Nuclear Collisions (35') X.Q. Luo

  8. Parallel talks at this conference • June 18 Afternoon (Lattice)  2:30---3:00 J.Verbaarschot (Stony Brook) Chiral symmetry breaking at nonzero chemical potential • June 18 Afternoon (RHIC)  2:00---2:30 N. Xu (LBL)Charm Production at RHIC 4:00—4:30  M. Huang (Tokyo U.) Resolving instabilities in gapless color superconductor X.Q. Luo

  9. II. Lattice Formulation Quark Gluon Lattice gauge theory (LGT) proposed by Wilson in 1974, is the most reliable technique for the investigation of phase transitions, from first principles. X.Q. Luo

  10. Continuum Yang-Mills action • replaced by the Wilson gluon action with β=6/g2 X.Q. Luo

  11. Continuum quark action • replaced by the discretized quark action where M is the discretized fermionic matrix. X.Q. Luo

  12. Naïve fermions: species doubling of fermion modes in the dispersion relation. Continuum fermions Naiver fermions: wrong X.Q. Luo

  13. No Go theorem: in any Local lattice theory with Chiral Symmetry, there exists species doubling of fermions. • AnySolutions to No Go theorem must violate Locality or Chiral Symmetry. X.Q. Luo

  14. Kogut-Susskind (staggered) fermions: • doubling reduced by ¼. • flavor symmetry × • chiral symmetry (only partially)√ • local √ , but might be problematic in • Wilson fermions: • no doubling • flavor symmetry√ • chiral symmetry × fine-tuning of the mass parameter has to be done • local √ • Ginsparg-Wilson (e.g. Overlap fermions proposed by Neuberger): • no doubling • flavor symmetry √ • chiral symmetry √ • locality × to expensive for dynamical fermions X.Q. Luo

  15. X.Q. Luo

  16. X.Q. Luo

  17. III. QCD at Finite Temperature and Chemical Potential In the Hamiltonian formulation of lattice QCD, this is well defined. Greogry, Guo, Kroger, X.Q. Luo, Phys. Rev.D62 (2000) 054508. Y. Fang, X.Q. Luo, Phys. Rev.D69 (2004) 114501. X.Q. Luo,Phys. Rev.D70（2004）091504(Rapid Commun.) X.Q. Luo

  18. In the Lagrangian formulation, this does not work. The vacuum energy density is divergent! X.Q. Luo

  19. Unfortunately So the fermionic determinant DetMis complex for any non-zero . This avoids Monte Carlo simulation with importance sampling: another No Go theorem. X.Q. Luo

  20. The recent years have seen enormous efforts on solving the complex action problem, and some very interesting information on the phase diagram for QCD with Kogut-Susskind (KS) fermions at large T and small μ has been obtained. Improved reweighting Imaginary chemical potential X.Q. Luo

  21. Lattice QCD with Imaginary Chemical Potential X.Q. Luo

  22. X.Q. Luo

  23. Deconfinement phase transition Nf=2 of KS fermions Nf=4 of KS fermions X.Q. Luo

  24. First Results from four flavors of Wilson fermions Wilson fermions: no doubling flavor symmetry√ chiral symmetry × fine-tuning of the mass parameter has to be done local √ X.Q. Luo

  25. First Results from four flavors of Wilson fermions Polyakov loop Chiral condensate X.Q. Luo

  26. First Results from four flavors of Wilson fermions: at TE<T X.Q. Luo

  27. First Results from four flavors of Wilson fermions: at TE<T The results above indicate that at higher T, there is Z(3) first order phase transition for QCD with Wilson quarks at imaginary chemical potential. Results above were obtained by scanning in this direction Now we scan in this direction X.Q. Luo

  28. First Results from four flavors of Wilson fermions: at intermediate quark mass and T<TE X.Q. Luo

  29. First Results from four flavors of Wilson fermions: at intermediate quark mass and T<TE X.Q. Luo

  30. First Results from four flavors of Wilson fermions: at intermediate quark mass, finiteT and real chemical potential X.Q. Luo

  31. First Results from four flavors of Wilson fermions: at intermediate quark mass, finiteT and real chemical potential X.Q. Luo

  32. First Results from four flavors of Wilson fermions: at intermediate quark mass, finiteT and real chemical potential Nature of the transition X.Q. Luo

  33. First Results from four flavors of Wilson fermions: at small or large quark mass and T<TE X.Q. Luo

  34. First Results from four flavors of Wilson fermions: at finiteT and real chemical potential X.Q. Luo

  35. First Results from two flavors of Wilson fermions: at small quark mass and T<TE X.Q. Luo

  36. First Results from lattice QCD with two flavors of Neuberger (Overlap) fermions at finite temperature, real chemical potential and strong coupling • Ginsparg-Wilson (e.g. Overlap fermions proposed by Neuberger): • no doubling • flavor symmetry √ • chiral symmetry √ • locality × X.Q. Luo

  37. First Results from lattice QCD with two flavors of Neuberger (Overlap) fermions at finite temperature, real chemical potential and strong coupling X.Q. Luo

  38. IV. Conclusion Four Flavors H.S. Chen, X.Q. Luo, "Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks," [hep-lat/0411023], to appear in Phys. Rev.D (2005). X.Q. Luo

  39. Two Flavors: First and Preliminary results from MC simulations of lattice QCD for two flavor QCD with Wilson quarks at imaginary chemical potential: second order at small quark mass, first order at large quark mass. H.S. Chen, X.Q. Luo, L.K. Wu, to be submitted. First results for QCD phase diagram from lattice QCD with two flavors of overlap (Neuberger) quarks at strong coupling: Second order phase transition at large T and small μ First order phase transition at large T and small μ X.L. Yu, X.Q. Luo, to be submitted. X.Q. Luo

  40. QCD Phase Diagram on the (T,μ) plane from lattice QCD Lagrangian Lattice QCD from Imaginary chemical potential method: de Forcrand, Lombardo, H. Chen, X.Q. Luo, L.K. Wu, … Multi-dimensional reweighting: Fodor and Katz, … Hamiltonian lattice QCD with Wilson quarks X.Q. Luo,Phys. Rev.D70（2004）091504(Rapid Commun.) X.L. Yu, X.Q. Luo, Lagrangian lattice QCD with Overlap (Neuberger) quarks CPPACS Bielefeld X.Q. Luo et al, making efforts Hamiltonian lattice QCD Greogry, Guo, Kroger, X.Q. Luo, Phys. Rev.D62 (2000) 054508.Y. Fang, X.Q. Luo, Phys. Rev. D69 (2004) 114501. X.Q. Luo

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