new results of canonical approach to finite density lattice qcd

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)


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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


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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


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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


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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


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T

ρ

Critical end point

coexistenthadrons

plasma

crossover


Phase diagramPhase diagramPhase diagramPhase diagram

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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


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Phase diagram (preliminary)Phase diagram (preliminary)Phase diagram (preliminary)Phase diagram (preliminary)


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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)



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Possible phase diagramPossible phase diagramPossible phase diagramPossible phase diagram

T

ρ

Critical end point

coexistenthadrons

plasma

crossover

????


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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

Documents

finite density simulations

larger lattice 63x4

normal nuclear matter

phase boundaryph

phase transitionsshape

new york

regensburgn2 simulation

critical end point