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?

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

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

Cost measurementsCost measurements

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

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

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

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

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

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

Continued FractionContinued Fraction

Want solution to

Use back-substitution – a 5D algorithm!

Equivalent to solving

Alternative 5D (N&N)Alternative 5D (N&N)

Naryanan&Neuberger 5D Operator. Want solution of

Solve 5D problem

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

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

Zolotarev vs. TanhZolotarev vs. Tanh

Zoom in – Show approx errorsZoom in – Show approx errors

Maximum error as approx. range increasesMaximum error as approx. range increases

Maximum error vs. LMaximum error vs. Lss

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:

OperatorsOperators

`CF' = Cont frac. 'M' = Möbius 'Z'=Zolotarev, 'T'=tanh

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

MMresres measurements per config measurements per config

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

Cost measurementsCost measurements

Cost measurementsCost measurements

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)