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Finite Density Simulation with the Canonical Ensemble

Explore baryon chemical potential, phase diagram, and critical end points in finite density simulation using canonical ensemble approach. Findings shed light on phase boundaries and crossover points in various flavor scenarios. Future plans include implementing improved actions and investigating critical points for three flavors.

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Finite Density Simulation with the Canonical Ensemble

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  1. Finite Density Simulation with the Canonical Ensemble Anyi Li, Xiangfei Meng, Andrei Alexandru, Keh-Fei Liu χQCD Collaboration

  2. Outline • Canonical approach • Observables • Baryon chemical potential • Possible phase diagram • Conclusion and future plans Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  3. Canonical Approach Grand canonical partition function Fugacity expansion Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  4. Canonical Approach Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  5. 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 Continues Fourier transform Useful for large k (see X. Meng talk on Tues 3:10pm – 3:30pm) WNEM Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

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

  7. Critical end point crossover Critical end point T T plasma plasma hadrons hadrons coexistent coexistent ρ ρ Phase Diagram Two flavors Four flavors ? Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  8. Phase Boundary Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62 Maxwell construction : determine phase boundary Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  9. Baryon Chemical Potential Nf = 4 Wilson gauge + fermionaction mπ~ 1 GeV Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  10. Maxwell Construction Nf = 4 Wilson gauge + fermion action Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

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

  12. Baryon Chemical Potential Nf = 2 Wilson gauge + fermion action Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  13. Critical end point T T plasma plasma hadrons hadrons coexistent coexistent ρ ρ Phase Diagram Two flavors Four flavors ? Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  14. Phase Diagram • “S-shape” is observed for Nf = 4 • “S-shape” is not observed down to 0.83Tc for Nf = 2 • Calculation at lower temperature is needed for two flavors Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  15. crossover Critical end point T plasma hadrons coexistent ρ Three Flavors Nf = 3 Iwasaki gauge + Clover fermionaction Lower quark mass ? Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  16. Three Flavors (Preliminary) Nf = 3 Iwasaki gauge + Clover fermionaction Lower quark mass Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

  17. Conclusion and Future Plans • Continuous Fourier transform makes larger density simulation feasible • First order is observed for four flavors below Tc • First order is not observed for two flavors down to 0.83Tc • Implement improved action. • Small quark mass • Look for “S-shape” and critical end point for three flavors Finite density simulation with the canonical ensemble Anyi Li - Lattice 2008 Williamsburg

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