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

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

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

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

Canonical approach Canonical ensembles Discrete Fourier transform 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

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

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

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

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

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

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

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

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

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

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

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

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