new results of canonical approach to finite density lattice qcd
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
New Results of Canonical Approach New Results of Canonical Approach to Finite Density Lattice QCDto Finite Density Lattice QCDNew Results of Canonical Approach New Results of Canonical Approach to Finite Density Lattice QCDto Finite Density Lattice QCD
Anyi Li, Andrei Alexandru, Keh-Fei Liu University of Kentucky
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• Canonical approachCanonical approach• Optimized discrete Fourier transform Optimized discrete Fourier transform • Reliable range of reweightingReliable range of reweighting• Possible phase diagram (preliminary)Possible phase diagram (preliminary)• ConclusionConclusion
OutlineOutlineOutlineOutline
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Standard HMCStandard HMC Accept/RejectAccept/Reject PhasePhase
Canonical approachCanonical approachCanonical approachCanonical approach
Hybrid Noisy Monte Carlo Hybrid Noisy Monte Carlo Hybrid Noisy Monte Carlo Hybrid Noisy Monte Carlo
Canonical ensemblesCanonical ensembles
Discrete Fourier transformDiscrete Fourier transform
K. F. Liu, K. F. Liu, QCD and Numerical Analysis QCD and Numerical Analysis Vol. III (Springer,New York, 2005),p. 101.Vol. III (Springer,New York, 2005),p. 101.Andrei Alexandru, Manfried Faber, Ivan Horva´th,Keh-Fei Liu, Andrei Alexandru, Manfried Faber, Ivan Horva´th,Keh-Fei Liu, PRDPRD 72, 114513 (2005) 72, 114513 (2005)
Exact determinant calculationExact determinant calculationExact determinant calculationExact determinant calculation
Andrei Alexandru, Andrei Alexandru, Finite density simulations using a determinant estimator Finite density simulations using a determinant estimator (Wed)(Wed)
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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• N/2 < simulation point.N/2 < simulation point.
can’t extract physics from simulationscan’t extract physics from simulations• N/2 = simulation point (symmetric point)N/2 = simulation point (symmetric point)
ln2 correction to the baryon chemical ln2 correction to the baryon chemical potentialpotential
• Optimized N = 2k +3Optimized N = 2k +3
minimal N, observables have little changes minimal N, observables have little changes while increasing Nwhile increasing N
Optimized discrete Fourier transformOptimized discrete Fourier transformOptimized discrete Fourier transformOptimized discrete Fourier transform
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Reliable range of reweightingReliable range of reweightingReliable range of reweightingReliable range of reweighting
Polyakov loopPolyakov loop
Baryon chemical potentialBaryon chemical potential
? Reweighting should be trusted within one baryon range? Reweighting should be trusted within one baryon range
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Reliable range of reweightingReliable range of reweightingReliable range of reweightingReliable range of reweighting
Polyakov loop (2 flavor Wilson action)Polyakov loop (2 flavor Wilson action)
0 5 10 150 .0
0 .5
1 .0
1 .5
k
P
D i r e c t s i m u l a t i o n s
k 6
k 3
k 0
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Reliable range of reweightingReliable range of reweightingReliable range of reweightingReliable range of reweighting
Baryon chemical potential Baryon chemical potential
0 5 10 150
1
2
3
4
5
6
7
k
T
D i r e c t s i m u l a t i o n s
k 6
k 3
k 0
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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T
ρ
Critical end point
coexistenthadrons
plasma
crossover
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
Phase diagramPhase diagramPhase diagramPhase diagram
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Phase diagramPhase diagramPhase diagramPhase diagram
Maxwell construction : determine phase boundaryMaxwell construction : determine phase boundary
Ph. Forcrand,S.Kratochvila, Ph. Forcrand,S.Kratochvila, Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62Nucl. Phys. B (Proc. Suppl.) 153 (2006) 62
Shinji Ejiri arXiv:0706.3549v1 [hep-lat]Shinji Ejiri arXiv:0706.3549v1 [hep-lat]
First order phase transition : two peaks in histogram of plaquetteFirst order phase transition : two peaks in histogram of plaquette
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Phase diagram (preliminary)Phase diagram (preliminary)Phase diagram (preliminary)Phase diagram (preliminary)
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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• 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 S-shape” is not clear, maybe due to quark is
heavyheavy• Phase transition ranges from 3.6 to 18 times the Phase transition ranges from 3.6 to 18 times the
normal nuclear matter density compared to the normal nuclear matter density compared to the results of results of Ph. Forcrand,S.Kratochvila (1 to 10)Ph. Forcrand,S.Kratochvila (1 to 10)
Phase diagramPhase diagramPhase diagramPhase diagram
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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Possible phase diagramPossible phase diagramPossible phase diagramPossible phase diagram
T
ρ
Critical end point
coexistenthadrons
plasma
crossover
????
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg
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• N can be optimized to 2k+3 in the simulationsN can be optimized to 2k+3 in the simulations• Up to 5 baryons reweighting (Up to 5 baryons reweighting (ββ=5.20) can be =5.20) can be
trustedtrusted• One baryon number reweighting is reliable One baryon number reweighting is reliable
(define baryon chemical potential)(define baryon chemical potential)• Implement improved action, small quark mass to Implement improved action, small quark mass to
see “S-shape” and critical end point see “S-shape” and critical end point • Finely scan phase diagram, simulate on larger Finely scan phase diagram, simulate on larger
lattice 6lattice 633x4, or even larger (Hybrid Noisy Monte x4, or even larger (Hybrid Noisy Monte Carol)Carol)
ConclusionConclusionConclusionConclusion
New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 New results of canonical approach to finite density lattice QCD Anyi Li - Lattice 2007 RegensburgRegensburg