格子QCDによる三体力
Takumi Doi(Nishina Center, RIKEN)• Motivation• 3NF in Lat QCD:
– Framework & comput. algorithm• Results for 3NF• Toward physical point calc on K:– Code tuning for 3NF & 2BF• Summary
2014/03/03

HPCII戦略プログラム分野５全体シンポジウム @ 秋葉原

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Motivation:
Nuclear Physics and Astrophysics from Lat QCDQCD Vacuum

BaryonFew-Body
NuclearForcesStandard Model

1st-principle lat calc.

分野５課題３

分野５課題２

分野５課題１

Nuclei

Neutron Star / Supernova

Ab-initio nuclear calc.
Lattice QCD predictions
play a crucial role

1st-principle lat calc.

Yamazaki et al.

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Three-nucleon forces (3NF)
What is 3NF ?

＋＋＋3NF: Forces whichcannot be explainedby pair-wise 2NF

2NF• Essential component forEoS at high density matter
3NF also play significant roles in◆ B.E. of light nuclei◆ Saturation point of nuclear m atter◆ N eutron rich nuclei

 N ucleosynthesis

RIBF @ RIKEN(R.Spero)

Neutron star Merger
SuperNova

3NF from NBS wave function[HAL QCD method]• Nambu-Bethe-Salpeter (NBS) wave function

NBS  Phase shift even in multi-particle system(non-rela limit)
S.Aoki et al., PRD88(2013)014036• Obtain 3NF throughby 2N calc

• NBS is obtained by 6pt. correlator
In practical calculation,
we employ time-dependent HAL QCD method
N.Ishii et al. (HAL QCD Coll.) PLB712(2012)437

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Challenge in multi-baryons on the lattice• Enormous computational cost for correlators– # of Wick contraction (permutations)– # of color/spinor contractions• Total cost:– 2H :– 3H :– 4He :

9 x
144 = 1 x 103
360 x 1728 = 6 x 105
32400 x 20736 = 7 x 108• [Unified contraction algorithm (UCA)]

t=t(sink)

t=t(src)

Improvement:
T.Yamazaki et al.,
PRD81(2010)111504

TD, M.Endres, CPC184(2013)117– Treat Wick/color/spinor contractions in a unified index space•  huge redundancies can be eliminated systematically•  permutation finished BEFORE any lattice calc
• Significant improvement

4He

<1sec
(x add’l. speedup)

See also subsequent works:

Detmold et al., PRD87(2013)114512
Gunther et al., PRD87(2013)094513

3NF calculation in Lat QCD

We fix the geometry of 3N ( this is not an approximation)

We study linear setup
(1)





We consider
Triton channel

(3)

(2)

 L(1,2)-pair = Ltotal = 0 or 2 only
 Bases are only three, labeled by 1S0, 3S1, 3D1 for (1,2)-pairLinear setup with various distance “r2”short “r2” setup

Study r2-dependence of 3NF

long “r2” setup

3N-forces (3NF) on the lattice
T.D. et al. (HAL QCD Coll.) PTP127(2012)723+ t-dep method updates etc.
Triton channel

short-range
repulsive 3NF !

Preliminary

Nf=2 clover (CP-PACS), 1/a=1.27GeV,
L=2.5fm, mπ=1.1GeV, mN=2.1GeV

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3N-forces (3NF) on the lattice
T.D. et al. (HAL QCD Coll.) PTP127(2012)723+ t-dep method updates etc.
Triton channel

short-range
repulsive 3NF !

Preliminary

Nf=2 clover (CP-PACS), 1/a=1.27GeV,
L=2.5fm, mπ=0.76-1.1GeV, mN=1.6-2.1GeV

Y dofYNN(?)

How about other geometries ?
How about YNN, YYN, YYY ?

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Toward physical point calc on K:
code tuning status• Physical quark mass configurations w/ L=9fm on K
– Configurations in generation• Comput. of Potential = quark solver + measurement– For usual lattice studies, solver is dominant– For baryon forces, measurement is very costlyΛΝ• Very expensive contraction cost, local comput. ΛΞ• Measurement– Three-nucleon forces (3NF)– Two-baryon forces (2BF)~x50 calc• Expensive contraction cost by many coupled channel systems• FFT cost by convolution (zero-mom projection for 2-body system)

Development in FY2013• Extensive refactoring of the code was performed– Unified Contraction Algorithm (UCA) for all 2BF: NN/YN/YY(in addition to 3NF)
– Many FFT are bundled to reduce the latency– Better implementation of OpenMP & cache tuning/SIMD• (Found a lot of system bugs (FX10/Kei, BG/Q, SR16000, etc.))– 2BF: ~ x10-x100– 3NF: ~ x1000

speedup

3NF: efficiency =18% @ 2048node• Comput. Cost as of the end of FY2013– Target: 96^4 in 2048node– Measurement (2BF): ~5mins for 16x2 time slices– Solver: ~16mins w/o AMA, ~4mins(?) w/ AMA–  measurement code becomes reasonably fastSummary and Prospects• Hadron Interactions by 1st principle Lat calc
– Bridging different worlds:
Particle Physics / Nuclear Physics / Astrophysics• Frontier: Three-Nucleon Forces (3NF)– NBS wave func. carries proper phase shifts !
– Breakthrough in compt. cost [unified contraction algorithm]– Repulsive 3NF at short distance observed• On the K computer:
UCA implemented for all 2BF & other code tunings
10PFlops

 Measurement reasonably fast Physical quark mass calc

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