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

2 Canonical approachCanonical approach Optimized discrete Fourier transformOptimized discrete Fourier transform Reliable range of reweightingReliable range of reweighting Possible phase diagram (preliminary)Possible phase diagram (preliminary) ConclusionConclusion OutlineOutline New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

3 Standard HMC Standard HMCAccept/RejectPhase Canonical approach Hybrid Noisy Monte Carlo Canonical ensembles Discrete Fourier transform K. F. Liu, QCD and Numerical Analysis Vol. III (Springer,New York, 2005),p Andrei Alexandru, Manfried Faber, Ivan Horva´th,Keh-Fei Liu, PRD 72, (2005) Exact determinant calculation Andrei Alexandru, Finite density simulations using a determinant estimator (Wed) New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

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

9 Maxwell construction : determine phase boundary Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62 Shinji Ejiri arXiv: v1 [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 Peak shifts shows the hint for phase transitionPeak shifts shows the hint for phase transition “S-shape” is not clear, maybe due to quark is heavy“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)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) Phase diagram New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

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

13 N can be optimized to 2k+3 in the simulationsN can be optimized to 2k+3 in the simulations Up to 5 baryons reweighting (β=5.20) can be trustedUp to 5 baryons reweighting (β=5.20) can be trusted One baryon number reweighting is reliable (define baryon chemical potential)One baryon number reweighting is reliable (define baryon chemical potential) Implement improved action, small quark mass to see “S-shape” and critical end pointImplement improved action, small quark mass to see “S-shape” and critical end point Finely scan phase diagram, simulate on larger lattice 6 3 x4, or even larger (Hybrid Noisy Monte Carol)Finely scan phase diagram, simulate on larger lattice 6 3 x4, or even larger (Hybrid Noisy Monte Carol) ConclusionConclusion New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg