Transcript Chiral Fermion Proposal

Hadron Structure using Dynamical Chiral
Fermions
A. Alexandru, B. Bistrovic, J. Bratt, R. Brower, M.
Burkardt, T. Draper, P. Dreher, R. Edwards, M.
Engelhardt, R. Irwin, G. Fleming, O. Jahn, K.-F. Liu, N.
Mathur, J. Negele, K. Orginos, J. Osborn, A. Pochinsky,
D. Renner, M. Musolf, D. Richards, D. Sigaev, A.
Thomas
Proposal
Dynamical chiral fermions:
Goal:
– Initial dyn. ensemble with small quark (and
residual) mass for hadron structure
– Test new actions/algorithms
– Understand/control mixing effects in hybrid
calculations
Which Action??
 LHPC/UKQCD - work with B. Joo, A. Kennedy,
K. Orginos, U. Wenger
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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
 Goal: choose a common 4D/5D fermion action
within RBC, UKQCD and USQCD for dyn.
simulations
 Coordinate simulations – different lattice sizes
 Share the datasets - may only be after public release
Status
 Collaborations with UKQCD
 Code & analysis development – strong connection
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Completed initial study of fermion actions
Now testing new methods in Nf=2+1 QCD
Intent to produce small quark mass ensemble
UK agreement:
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Use of < 10% resources (~ 1 rack) under algorithm devel.
Use in conjunction with USQCD resources and share lattices
Strong interest within UKQCD to pursue improved methods
Clear Edinburgh focused on short-term results
New methods used in a second/later phase of running
 RBC:
 Interested, but man-power constrained
 UK+RBC:
 Currently tweaking run-time params for DWF
Goal: Overlap operator
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Overlap operator on the lattice:
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Four dimensional space of algorithms:
– Kernel:
– Approximation:
– Representation (CF – Continued Fraction, PF -
Partial Fraction, DWF=CT=Cayley Transform)
– Contraint (5D, 4D)
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Only 4D operator physically relevant:
Kernel
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Choice of kernel affects ``physics’’ (cutoff effects)
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Wilson kernel
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Shamir kernel
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Mobius kernel
Approximations
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Two popular approximations
 Polar (“tanh”) [induced by DWF]
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Zolotarev: (analytic form of my old Remez solution)
sn(z/
M,λ)
sn(z
,k)
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Trick – projection: supplement approx. with exact eigenv.
Representations
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Continued Fraction – Euler representation, i determine
approx.
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Partial Fraction:
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Cayley Transform:
Example: Continued Fraction
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Want solution to
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Use back-substitution – a 5D algorithm!
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Equivalent to solving
5D Operator – Generic Case
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Want solution to
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Representation for (H) turned into 5D system
Chiral Symmetry Breaking
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Defect of Ginsparg-Wilson relation
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Using Overlap operator D(0)=(1/2)(1+5(H)) ,
L measures chiral symmetry breaking
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Can show usual DWF mres
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mres just one matrix element of operator L
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Goal: want small mres for small cost
Spectral Flow
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HW  -M Eigenvalue Flow
  5.85, 63 12
Topological charge is deficit of
states of H(-M)
 Spectral flow counts zero
crossings to find deficit at
some M
 Dov(0) should have 0 evs when
Q != 0
Edwards, Heller, Narayanan 97
Overlap(Hw) spectral flow for smooth SU(2)
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Spectral flow of overlap Ho(m) = 5 Do(m), H=Hw(-m)
Single instanton, 84, Dirichlet BC, r=1.5, cm = 4.5.
The zero modes after the crossing, m=0.6, 0.7, and 0.8.
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The continuum solution
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DWF Spectral Flow
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DWF (and other reps!) should have zero eigenvalues at Q != 0
Without projection (enforcement of exact -sym), zero evs
slowly arise
-sym breaking from nearby zero-crossings (topology
change)
DWF
Projected DWF
Spectral flow in SU(3): typical case
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Spectral flow of H(m) quenched
Wilson =5.85, 6.0
 50 configs, 10 evs overlayed
 Fill-in by small modes
 What about mres?
 Two basic scales: r(c) (where
band stops), r(0)
 mres affected by:
– Dense band below approx region
– Evs piling near 0
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Goal: choose approx. below
dense band.
Need projection for r(0)
Tests
Chiral Fermion Working Group:
 Use Nf=2 DWF ensembles (RBC), m = 500 MeV
 Actions (D(0)=(1/2)(1+5(H))
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Mobius : (Rescaled) Shamir (H=HT) and Overlap (H=Hw)
Continued Fraction rep. for (Hw) in 5D form
Different actions with same 4D physics (H)
Reduce mres by better approx. of (x)
Zolotarev (Chebyshev) and
tanh approx. to (x)
Results – Cost Comparisons
 Of actions tested, standard DWF Shamir is least effective.
 Zolotarev Continued Fraction (Hw and HT) are candidates
Second Moment
 Second norm not crazy – shows not wild cancellations in mres
 Zolotarev Continued Fraction (Hw and HT) are good candidates
Forces in HMC
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Comparison of MD forces in
Nf=2 DWF [QCDOC]
Forces cancel in combined
fermion force term
Gauge force MUCH noisier!!
F*t relevant scale
Can exploit multi-time scale
integrators!!
Speed integration since gauge
is cheap!
Explains RBC result – no mass
dependence on step-size
3-Flavor – DWF
Comparison of Nf=2+1 DWF to Cont. Frac.
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UKQCD – Iwasaki, =2.2, Nf=3, mf=0.04,
a-1 ~ 1.6 – 1.8 GeV, a*m ~ 0.5
Dyn. calc at
Ls=8, mres ~ 0.006
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mres / mf > 10% at large pion mass
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Tune Cont. Frac (Hw) to same Ls=8 DWF
pion mass
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3-Flavor – Continued Fraction
Forces in Nf=2+1 HMC, +1 via
RHMC
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Gauge force noisy. Use improved
integrator
Sexton-Weingarten – fine-step
integration in gauge action
Combine with new Takaishi-de
Forcrand Integrator
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Factor of ~ 3 speed-up
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Spikes – possible instability
or topology change?
3-Flavor – Continued Fraction (Hw)
UKQCD – Iwasaki, =2.2, DWF,
Nf=3, mf=0.04, a*m ~ 0.5,
a-1 ~ 1.6 – 1.8 GeV
Dyn. calc at
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Ls=8, mres ~ 0.006
Chroma – Iwasaki, =2.2, Nf=3,
mf=0.024, a*m ~ 0.5
Valence Ls
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Ls=12, mres ~ 0.0025
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Ls=24, mres ~ 0.0004
Dyn. calc at
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Ls=6, mres*0.04/0.024 = 0.0034(2)
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Ls=8, mres*0.04/0.024 = 0.00044(5)
Nf=2+1 Cont. Frac.
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Can achieve small mres via improved
approximation!!!
Cost roughly the same
Future
 Actions:
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For valence calcs – use current improved methods
Very early phase of dyn. fermion development
Can have same physics with different 5D actions
Use improved methods for small quark mass (?)
 Algorithms:
 Many algorithm tricks to test
 Can improve algorithm without changing physics
Taste Breaking Effects
 Have/producing large Asqtad data sets
 Current work (Negele proposal) using DWF on Asqtad
 Taste breaking study:
 Compare fully chiral physics observables with hybrid
calcs
 Disentangle taste breaking effects on hybrid calcs
 Leverage small allocation to produce low quark mass, high
statistics and volume hadronic observables (JLab)
 Nucleon structure functions and (generalized) form-factors
Code Status
 All action tests done in Chroma (JLab, UK IBM’s, BGL)
 Valence calcs (spectro, 3pt) in production at JLab
 HMC
 Nf=2+1 HMC/RHMC in production - 4D even/odd prec,
combined force term
 Support HMC Mobius, Cont. Frac., Partial Frac - generic
H(b5,c5)
 Move to use 4D pseudofermions (instead of current 5D)
 Stand-alone inverters generically ~25% peak, double prec.
 Improve 5D Dirac op – use ``vector’’ dslash calls ~ 35%
Machine Status
 QCDOC running began ~ May 1, 2005
 1K Rack UK, 1K US, ~ 1 mother-board (MB) US
 BNL QCDOC:
 Allocated rack18: still flaky – lost time due to strange unresolved
pass-through problems
 Most results from UK rack and 1 US MB.
 Access to MB’s still tough – since last weekend 6 available.
 QOS 2.5.9 memory prevents production on single racks
 Disk IO performance, /host, slow – require disk arrays
 Network problematic – lost connections (qdaemon). Work
around in place.
 Nothing unexpected for an alpha user!!
 Support staff very helpful! Thanks to Chulwoo J. and Stratos E.
Future
 Actions:
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For valence calcs – use current improved methods
Very early phase of dyn. fermion development
Can have same physics with different 5D actions
Use improved methods for small quark mass (?)
 Algorithms:
 Many algorithm tricks to test
 Can improve algorithm without changing physics