Chiral restoration and deconﬁnement in two-color QCD with ...theorie.ikp.physik.tu-darmstadt.de/~dscheff/talk.lattice2013.pdf · Motivation effective Polyakov loop potential É

Chiral restoration and deconfinement in two-colorQCD with two flavors of staggered quarksDavid Scheffler, Christian Schmidt, Dominik Smith,Lorenz von Smekal

É Motivation

É Effective Polyakov loop potential

É Chiral properties

É Summary and outlook

2013/08/02 | Lattice 2013 | D. Scheffler | 1

Motivation

effective Polyakov loop potentialÉ influence of quarks on Polyakov loop

potential

É compare to effective modeldescriptions

É two-color QCD as QCD-like theorywhere finite density is accessible

chiral properties

É scale setting

É scaling behavior

0 200 400 600 800

µq (MeV)

0

50

100

150

200

250

T (

MeV

)

0 0.2 0.4 0.6 0.8µa

24

16

12

8N

τ

BEC?

BCS?

Quarkyonic

QGP

Hadronic

<qq>

<L>

Boz, Cotter, Fister, Mehta, Skullerud [1303.3223]

0

50

100

150

200

250

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

T [M

eV

]

µ [mπ]

Φ infl. pt.Φ susc.

σ half valueΦ half value

diquark cond.

Strodthoff, von Smekal [1306.2897]


Effective Polyakov loop potential

É per-site probability distribution P(l) via histogram

É per-site “constraint” effective potential:

V0(l) =− log P(l)

É obtain the actual per-site effective potential via Legendre transform

W (h) = log

∫

dl exp�

−V0(l) + hl�

Veff(l̂) = suph

�

l̂h−W (h)�


Polyakov Loop distributions and effective potenti-als at β = 2.577856

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-1 -0.5 0 0.5 1

P(L

)

L

Nt=12 T/Tc=0.83Nt=10 T/Tc=1.00Nt=8 T/Tc=1.25Nt=6 T/Tc=1.67

0

0.5

1

1.5

2

2.5

3

-1 -0.5 0 0.5 1

V_0

(L)

L


É pure gauge results by Smith, Dumitru, Pisarski, von Smekal [1307.6339]

É fixed scale


Polyakov Loop distributions and effective potenti-als at β = 2.577856

0

1

2

3

4

5

6

-1 -0.5 0 0.5 1

Veff

(L)

L


0

0.5

1

1.5

2

2.5

3

-1 -0.5 0 0.5 1

V_0

(L)

L


É pure gauge results by Smith, Dumitru, Pisarski, von Smekal [1307.6339]

É fixed scale


Polyakov Loop distributionsat β = 2.577856

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-1 -0.5 0 0.5 1

P(L

)

L

solid: pure gaugedashed: am=0.5dotted: am=0.1


É add N f = 2 staggered quarks β = 2.635365

É neglect scale change through quark masses


Polyakov Loop effective potentialat β = 2.577856

0

0.5

1

1.5

2

2.5

3

-1 -0.5 0 0.5 1

V_0

(L)

L

solid: pure gauge

dashed: am=0.5

dotted: am=0.1


β = 2.635365



0

1

2

3

4

5

6

-1 -0.5 0 0.5 1

Veff

(L)

L

solid: pure gauge

dashed: am=0.5

dotted: am=0.1



Modeling the distributions and potentialsFit coefficients at β = 2.577856

É pure gauge: for T ≤ Tc : Vandermonde potential:

V (Tc)0 (l) =−

1

2log(1− l2)− C P(Tc)(l) =

2

π

p

1− l2

É ansatz for T > Tc : V0(l) = V (Tc)0 (l) + a(T )− b(T )l + c(T )l2

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

dis

trib

uti

on P

(l)

Polyakov loop l

Nt=6, Ns=24, ma=0.1, beta=2.577856

datafit

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

dis

trib

uti

on P

(l)

Polyakov loop l

Nt=12, Ns=48, ma=0.5, beta=2.577856

datafit


Modeling the distributions and potentialsFit coefficients at β = 2.577856

É pure gauge: for T ≤ Tc : Vandermonde potential:

V (Tc)0 (l) =−

1

2log(1− l2)− C P(Tc)(l) =

2

π

p

1− l2

É ansatz for T > Tc : V0(l) = V (Tc)0 (l) + a(T )− b(T )l + c(T )l2

0

0.02

0.04

0.06

0.08

0.1

0.8 1 1.2 1.4 1.6 1.8 2

fit

coeffi

cient

a

T/Tc

pure gaugema=0.5ma=0.1

0

0.2

0.4

0.6

0.8

1

1.2

0.8 1 1.2 1.4 1.6 1.8 2

fit

coeffi

cient

b

T/Tc

0

0.05

0.1

0.15

0.2

0.25

0.8 1 1.2 1.4 1.6 1.8 2fit

coeffi

cient

cT/Tc

β = 2.635365


Chiral propertiesSimulation setup

É N f = 2 staggered quarks via RHMC

É Nt = 4,6, 8 with aspect ratio Ns/Nt = 4É several masses am= 0.005,0.01, 0.02,0.1, . . .É finite temperature: vary β

symmetry breaking

É continuum: SU(2N f )→ Sp(N f )É staggered: SU(2N f )→ O(2N f ), here: SU(4)' O(6)→ O(4)


Order parameters

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1.4 1.6 1.8 2 2.2 2.4

chir

al co

ndensa

te

beta

Nt=4 Ns=16

m/T=0.02m/T=0.04m/T=0.08

m/T=0.4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1.4 1.6 1.8 2 2.2 2.4

Poly

ako

v loop

beta

Nt=4 Ns=16

m/T=0.02m/T=0.04m/T=0.08

m/T=0.4


Order parameters

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1.4 1.6 1.8 2 2.2 2.4

chir

al co

ndensa

te

beta

Nt=6 Ns=24

m/T=0.03m/T=0.06m/T=0.12

m/T=0.6

0

0.05

0.1

0.15

0.2

0.25

1.4 1.6 1.8 2 2.2 2.4

Poly

ako

v loop

beta

Nt=6 Ns=24

m/T=0.03m/T=0.06m/T=0.12

m/T=0.6


Order parameters

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1.4 1.6 1.8 2 2.2 2.4

chir

al co

ndensa

te

beta

Nt=8 Ns=32

m/T=0.04m/T=0.16

m/T=0.6m/T=0.8

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1.4 1.6 1.8 2 2.2 2.4

Poly

ako

v loop

beta

Nt=8 Ns=32

m/T=0.04m/T=0.16

m/T=0.6m/T=0.8


Chiral susceptibilities

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

1.6 1.7 1.8 1.9 2 2.1 2.2

chir

al su

scepti

bili

ty

beta

Nt=4 Ns=16

m/T=0.02m/T=0.04m/T=0.08

m/T=0.4

0

0.5

1

1.5

2

2.5

3

3.5

4

1.8 1.9 2 2.1 2.2 2.3

chir

al su

scepti

bili

ty

beta

Nt=6 Ns=24

m/T=0.03m/T=0.06m/T=0.12

m/T=0.6

0

0.5

1

1.5

2

2.5

1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3

chir

al su

scepti

bili

ty

beta

Nt=8 Ns=32

m/T=0.04m/T=0.16

m/T=0.6m/T=0.8


Chiral susceptibilities

3.5

4

4.5

5

5.5

6

1.855 1.86 1.865 1.87 1.875 1.88 1.885 1.89 1.895

chir

al su

scep

tib

ility

beta

Nt=4 Ns=16, am=0.005

datafrom F-S reweighting


Temperature scale

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

0 0.1 0.2 0.3 0.4 0.5 0.6

beta

m/T

Nt=4Nt=6Nt=8

fits

chiral extrapolation

βpc(m, Nt) = βc(Nt) + b · amc


Temperature scale

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

0 0.1 0.2 0.3 0.4 0.5 0.6

beta

m/T

Nt=4Nt=6Nt=8

fits

chiral extrapolation

βpc(m, Nt) = βc(Nt) + b · amc

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

2 3 4 5 6 7 8 9

beta

Nt


Temperature scale

leading scaling behavior:T

Tc= exp {b(β − βc)}

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

beta

log(Nt/4)

From linear fit:

b = 3.18 +- 0.30

Nt=4

Nt=6

Nt=8

datafit


magnetic scaling

χmax ∼ m1/δ−1

1

10

100

1000

0.01 0.1 1

delta = 4.0

5.5(7)

5.1(4)

chir

al su

scepti

bili

ty /

T^

2

m/T

Nt=4Nt=6Nt=8

fits


Summary and outlook

Summary

É unquenched effective Polyakov loop potentials

É began scale setting and determine critical exponents

OutlookÉ continue: chiral properties need more work, especially at Nt = 8É main goal: effective Polyakov loop potentials at finite density

É possible direction: adjoint representation


Backup Slides


Fixed scale parameters

É pure gauge analysis: Smith, Dumitru, Pisarski, von Smekal [hep-lat/1307.6339]

β apσ Nt T/Tc

2.577856 0.140 12 0.8310 1.008 1.256 1.67

2.635365 0.116 12 1.0010 1.208 1.506 2.00

T (Nt) =1

Nt a

β am

2.577856 0.50.1

2.635365 0.4140.083


Polyakov Loop distributionsat β = 2.635365

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-1 -0.5 0 0.5 1

P(L

)

L

solid: pure gaugedashed: am=0.414dotted: am=0.083


β = 2.577856



0

0.5

1

1.5

2

2.5

3

-1 -0.5 0 0.5 1

V_0

(L)

L

solid: pure gauge

dashed: am=0.414

dotted: am=0.083


β = 2.577856


Fit coefficientsat β = 2.635365

0

0.02

0.04

0.06

0.08

0.1

0.8 1 1.2 1.4 1.6 1.8 2

fit

coeffi

cient

a

T/Tc

pure gaugema=0.414ma=0.083

0

0.2

0.4

0.6

0.8

1

1.2

0.8 1 1.2 1.4 1.6 1.8 2

fit

coeffi

cient

b

T/Tc

0

0.05

0.1

0.15

0.2

0.25

0.8 1 1.2 1.4 1.6 1.8 2

fit

coeffi

cient

c

T/Tc

V0(l) = V (Tc)(l) + a(T )− b(T )l + c(T )l2

β = 2.577856


Finite volume testNt = 8, am= 0.5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

2.35 2.4 2.45 2.5 2.55 2.6

beta

finite size comparison for Nt=8, ma=0.5

P.loop Ns=16P.loop Ns=24P.loop Ns=32

Ch.cond. Ns=16Ch.cond. Ns=24Ch.cond. Ns=32

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

dis

trib

uti

on

Polyakov loop value

finite size comparison for Nt=8, am=0.5

beta=2.577856

Ns=16Ns=24Ns=32

0.1 0.2 0.3 0.4 0.5



0

0.02

0.04

0.06

0.08

0.1

0.12

2 2.05 2.1 2.15 2.2

beta


P.loop Ns=8P.loop Ns=16P.loop Ns=24P.loop Ns=32

Ch.cond. Ns=8Ch.cond. Ns=16Ch.cond. Ns=24Ch.cond. Ns=32

0

0.5

1

1.5

2

2.5

3

2 2.05 2.1 2.15 2.2

beta


Ch. susc. Ns=8Ch. susc. Ns=16Ch. susc. Ns=24Ch. susc. Ns=32



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

dis

trib

uti

on

Polyakov loop value


beta=2.0Ns=8Ns=16Ns=24Ns=32

-0.2 -0.1 0 0.1 0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

dis

trib

uti

on

Polyakov loop value


beta=2.2Ns=8Ns=16Ns=24Ns=32

-0.2 -0.1 0 0.1 0.2


Documents

Chiral restoration and deconﬁnement in two-color QCD with ...theorie.ikp.physik.tu-darmstadt.de/~dscheff/talk.lattice2013.pdf · Motivation effective Polyakov loop potential É