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New Results of Canonical Approach to Finite Density Lattice QCD

New Results of Canonical Approach to Finite Density Lattice QCD. Anyi Li, Andrei Alexandru, Keh-Fei Liu University of Kentucky. Outline. Canonical approach Optimized discrete Fourier transform Reliable range of reweighting Possible phase diagram (preliminary) Conclusion.

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New Results of Canonical Approach to Finite Density Lattice QCD

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  1. New Results of Canonical Approach to Finite Density Lattice QCD Anyi Li, Andrei Alexandru, Keh-Fei Liu University of Kentucky

  2. Outline • Canonical approach • Optimized discrete Fourier transform • Reliable range of reweighting • Possible phase diagram (preliminary) • Conclusion New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  3. 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) Canonical ensembles Discrete Fourier transform Standard HMC Accept/Reject Phase Hybrid Noisy Monte Carlo Andrei Alexandru, Finite density simulations using a determinant estimator (Wed) Exact determinant calculation New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  4. Optimized discrete Fourier transform • N/2 < simulation point. can’t extract physics from simulations • N/2 = simulation point (symmetric point) ln2 correction to the baryon chemical potential • Optimized N = 2k +3 minimal N, observables have little changes while increasing N New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  5. Reliable range of reweighting Polyakov loop Baryon chemical potential ? Reweighting should be trusted within one baryon range New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  6. Reliable range of reweighting Polyakov loop (2 flavor Wilson action) New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  7. Reliable range of reweighting Baryon chemical potential New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  8. crossover Critical end point T plasma hadrons coexistent ρ Phase diagram New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  9. Phase diagram Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62 Maxwell construction : determine phase boundary Shinji Ejiri arXiv:0706.3549v1 [hep-lat] First order phase transition : two peaks in histogram of plaquette New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  10. Phase diagram (preliminary) New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  11. Phase diagram • Peak shifts shows the hint for phase transition • “S-shape” is not clear, maybe due to quark is heavy • Phase transition ranges from 3.6 to 18 times the normal nuclear matter density compared to the results of Ph. Forcrand,S.Kratochvila (1 to 10) New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  12. crossover Critical end point T plasma hadrons coexistent ρ Possible phase diagram ? New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

  13. Conclusion • N can be optimized to 2k+3 in the simulations • Up to 5 baryons reweighting (β=5.20) can be trusted • One baryon number reweighting is reliable (define baryon chemical potential) • Implement improved action, small quark mass to see “S-shape” and critical end point • Finely scan phase diagram, simulate on larger lattice 63x4, or even larger (Hybrid Noisy Monte Carol) New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

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