dynamical chiral fermions the `grail’ – dyn. chiral fermions generation of dyn. chiral fermions...
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Dynamical Chiral FermionsDynamical Chiral Fermions
The `Grail’ – dyn. chiral fermions Generation of dyn. chiral fermions configs
– RBC on the RIKEN QCDOC – Jan 05 (some %)– UKQCD on the UK QCDOC – Jan 05 (some %)– RBC on the US QCDOC – April 05 (probably some %)
Given certain existence of dyn. chiral configs via large scale simulations – NOT AN EXPLORATORY PROJECT
Good physics?– Good chiral control – no taste breaking, avoid valence smearing– C. Bernard in May SciDAC : DWF0 < MILC2 in “cost”– A question of when to jump to dyn. chiral ferm.
How to leverage off world efforts?
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Which Action??Which Action??
LHPC/UKQCD - work with B. Joo, A. Kennedy, K. Orginos, U. Wenger Evaluate “cost” of various chiral ferm actions Consider only 5D inverters for use in force term in HMC No projection – have residual mass Decide by a metric – cost for fixed mres
Results being presented at RBC/UKQCD meeting
Goal: choose a common fermion action within RBC, UKQCD and LHPC for dyn. simulations Coordinate simulations – different lattice sizes??? Each group leverages off other for more resources (like MILC) Share the datasets - early access before public domain
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ResultsResults
Chiral Fermion Working Group: Results:
Of actions tested, standard DWF Shamir is clear loser. Zolotarev Continued Fraction is ``winner’’ (caveats,
though). Second is rescaled Shamir DWF via Mobius (tanh) Zolo. DWF actions needed for final decision
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Cost measurementsCost measurements
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RecommendationsRecommendations
Chiral Fermion Working Group: Recommendations:
Suggest RBC (small) change to Mobius (force term and energy) Big picture – what to have for overlap induced kernel? If Wilson kernel used
Cont. Frac - optimal valence action! Nominal sea mres and tiny valence mres (Golterman & Shamir) Cross-over usage by overlap-ers Possible 4D pseudofermion HMC with Cont. Fract. for force term
If Shamir kernel used No cross-over to overlap Not optimal inverter Projection problematic???
Recommend Wilson kernel Continue to reduce chiral sym. breaking
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FutureFuture Algorithms:
Pursue efficacy of projection and smearing 4D pseudofermion HMC Instead 5D HMC via Alternating-Schwarz??
Coordination: Prefer share configs internally. RBC – only available once public?
Collaborations: LHPC/UKQCD –
Code & analysis development – strong connection Major overlap on hadronic physics – work together?? UKQCD – wait and see
LHPC/UKQCD/RBC ?? Many issues raised
RBC/UKQCD Only agreed to share Columbia 2K nodes (Asqtad)
RBC and UKQCD cases Strong interest generated only from algorithm work
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AllocationsAllocations Nominally Nuc. Phys. 1/3 of US
– By Apr 05 total 8 TFlops in US (currently 0.5 at JLab)– Use some % allocation of NP for dyn. chiral instead of staggered ?– E.g., finish a=0.13fm DWF/Asqtad and do instead dyn. chiral??
Propose a dyn. chiral m=300, 353, 500 MeV, 28^3x32, a=0.11fm
– Cost=2.4 TfY for 10k traj – use half (like MILC) – total 1.2 Tflop-Y– Possibly coordinate a 243£32 with RBC or UKQCD?
Cost in Tflop-Years of 10K traj., of dyn. chiral ferm generation
m(Mev) 250 300 353 500
Volume N5 a (fm) Tflop-Y
243£ 32 6 0.11 1.3 0.75 0.46 0.16
283£ 32 2.3 1.3 0.82 0.29
323£ 32 3.8 2.2 1.35 0.47
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Dynamical Fermion - AllocationsDynamical Fermion - Allocations
Propose a dyn. chiral m=300, 353, 500 MeV, 24^3x64, a=0.11fm, L=2.64fm– Cost=2.35 TfY for 5k traj– Possibly coordinate with UKQCD, RBC & U.S. HEP?
Cost in Tflop-Years of 5K traj., of dyn. chiral ferm generation
m(Mev) 250 300 353 (400) 500
243£ 64 N5=8
Tflop-Y 2.2 1.3 0.78 (0.54) 0.27
m L 3.3 4.0 4.7 (5.3) 6.6
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The GoalThe Goal
Overlap operator on the lattice
Choice of H, e.g., H=Hw(-M)=5 Dw(-M)
We approximate (H) by rational function where Pn(H), Qm(H) poly. in H of degree n and m
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RepresentationsRepresentations
Partial Fraction: (``4D Overlap – Inner CG’’)
Alternative 5D (N&N) (hybrid of Cont. Frac and gauss int.) Continued Fraction – Euler representation, i determine
approx.
Equivalence transformations
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Continued FractionContinued Fraction
Want solution to
Use back-substitution – a 5D algorithm!
Equivalent to solving
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Alternative 5D (N&N)Alternative 5D (N&N)
Naryanan&Neuberger 5D Operator. Want solution of
Solve 5D problem
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5D Domain Wall5D Domain Wall Domain wall action: 5D Domain wall kernel:
with quark mass , and
Integrate out Ls-1 extra fields to obtain
Here P is such that (P-1 )1 = q is the light fermion
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Induced 4D action – truncated overlapInduced 4D action – truncated overlap
Core piece of induced kernel:
Case of i=1
In general:
– Domain wall: H = HT = 5 Dw /(2 + a5 Dw), b5-c5=a5
– Overlap: H = Hw = 5 Dw , b5-c5=0
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Zolotarev vs. TanhZolotarev vs. Tanh
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Zoom in – Show approx errorsZoom in – Show approx errors
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Maximum error as approx. range increasesMaximum error as approx. range increases
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Maximum error vs. LMaximum error vs. Lss
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ComparisonsComparisons
Use RBC Dyn. Nf=2 DWF, a=0.11fm, 163£32, m=500 MeV
15 configs. Tune actions to same m- mass renorm.
Metric – compare Cost (D_w apps) and rescaled mres
Pion mass:
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OperatorsOperators
`CF' = Cont frac. 'M' = Möbius 'Z'=Zolotarev, 'T'=tanh
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Chiral Symmetry Breaking Chiral Symmetry Breaking
Defect of Ginsparg-Wilson relation
Using Overlap operator D(0)=(1/2)(1+5(H)) ,
L measures chiral symmetry breaking
Can show usual DWF mres
mres just one matrix element of operator L
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MMresres measurements per config measurements per config
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Density of EigenvaluesDensity of Eigenvalues
Compare EV’s of L
Tanh cumulative error saturates quickly
Zolo error can go negative!
Densities are what matters
Stretching Zolo approx. magnifies errors and mres
Can have neg. mres
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Cost measurementsCost measurements
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Cost measurementsCost measurements
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ConclusionsConclusions
Results: Of actions tested, standard DWF Shamir is clear loser. Zolotarev Continued Fraction is ``winner’’ (caveats,
though). Second is rescaled Shamir DWF via Mobius (tanh) Zolo. DWF actions needed for final decision
Suspect need test of N&N 5D method (almost ready)