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New Results of Canonical Approach to Finite Density Lattice QCD

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New Results of Canonical Approach to Finite Density Lattice QCD

Anyi Li, Andrei Alexandru, Keh-Fei Liu

University of Kentucky

- 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

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

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

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

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

Reliable range of reweighting

Baryon chemical potential

New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

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

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

Phase diagram (preliminary)

New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 Regensburg

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

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

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