New Mexico State University & Vienna University of Technology work in progress, in coop. with Michael Engelhardt 25. Juni 2014
non-trivial QCD vacuum project out important degrees of freedom start with minimal set of d.o.f. / model start with vortex-only (Z(2)) configs try to approach full theory and keep the vortex structure smooth vortex configs for gluonic & fermionic operators comes down to minimizing non-trivial (vortex) plaquettes 1000 Luescher-Weisz SU(2) configs, 8 4,β = 3.3
A plaquette is pierced by a P-vortex, if the product of its center projected links gives ½. center vortex in one dimension center-projected (P-vortex plaquettes) smearing going back, locality, gauge invariance 1 1/3 1/3 1/3
Standard Routines 0.2 0.15 0.1 0.05 0-0.05-0.1-0.15-0.2 MCG projected U(1) smeared SU(2) smeared + 1 HYP steps + 2 HYP steps + 3 HYP steps + 5 HYP steps original SU(2)
Flux Distribution a c a,c b d e iπ/8 e iπ/8 i e π e iπ/8 e iπ/2 iπ/8 e e iπ iπ /8 iπ/8 e e iπ/2 e e iπ/8 e iπ/8 b,d
2-fold refinement 2 4 x more lattice points, links & plaqs but only 8 x more neg. links and 4 x more vortex plaqs
- - b a c
Link Rotation smoother rotations on refined lattices problem of even/odd lattice slices
Flux a c b d leave original links untouched and spread vortex flux within the original plaquette 2D gauge transformations/rotations i.o. to minimize affected plaquettes
vortex-only Z(2) refined smeared SU(2) (smeared) vortex structure is not preserved...
(smoothing thin vortex surface ) refine Z(2) lattice configuration identify vortex plaquettes, Tr U µν = 1 refined link rotation smearing or refined flux distribution smearing (vortex smeared blocking) a) 6 plaquettes 0 plaquettes b) 5 plaquettes 1 plaquette c) 4 plaquettes 2 plaquettes d) 4 plaquettes 2 plaquettes
Overlap Spectra 0.4 0.3 λ 0.2 0.1 0-0.1-0.2-0.3-0.4-0.5 projected Z(2) link rotation -"- blocked flux distribution -"- blocked original SU(2)
Topological Susceptibility susceptibility Χ 1/4 [MeV] 400 350 300 250 200 150 Original (full) SU(2): vortex top.charge Q V fermionic Q F (overlap) gluonic Q T after cooling gluonic Q T after smearing flux smearing: vortex top.charge Q V fermionic Q F (overlap) gluonic Q T after cooling gluonic Q T after smearing Q V after revsmear blocking Q F after revsmear blocking Q T after blocking + cooling Q T after blocking + smearing 100 vortex blocking and smoothing
Topological Susceptibility susceptibility Χ 1/4 [MeV] 260 240 220 200 180 160 Original (full) SU(2): vortex top.charge Q V fermionic Q F (overlap) gluonic Q T after cooling gluonic Q T after smearing flux smearing: vortex top.charge Q V fermionic Q F (overlap) gluonic Q T after cooling gluonic Q T after smearing Q V after revsmear blocking Q F after revsmear blocking Q T after blocking + cooling Q T after blocking + smearing 140 a=0.3fm a=0.6fm
Topological Charge 4 4 blocked flux smeared Q 2 0-2 blocked flux smeared Q 2 0-2 -4 fermionic Q F gluonic Q T -4-4 -2 0 2 4 original Q original Q F vs. smeared Q T original Q T vs. smeared Q F -4-2 0 2 4 original Q fermionic, cooling, smearing vs. vortex topological charge instanton vs. center vortex degrees of freedom
- eigenmode - correlation eigenmode correlation 2.5 2 1.5 1 0.5 projected Z(2) link rotation -"- blocked flux distribution -"- blocked original SU(2) 0-0.5 0 2 4 6 8 10 12 number of attached vortex plaquettes
limited Wilson loops 1 W x /W 0 0-1 0 20 40 60 80 100 Wilson loop area W 2 /W 0 original W 2 /W 0 link rot W 2 /W 0 -"- block W 2 /W 0 flux dist W 2 /W 0 -"- block W 1 /W 0 original W 1 /W 0 link rot W 1 /W 0 -"- block W 1 /W 0 flux dist W 1 /W 0 -"- block
Creutz Ratios String Tension Χ(R,R) 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 original SU(2) link rotation -"- blocked flux distribution -"- blocked asymptotic string tension -0.05 0 1 2 3 4 5 R
Classical Configuration y y z z y x x y z z
smeared center vortices keeping their structure removed the eigenvalue gap for overlap fermions reproduced gluonic and fermionic observables topological (charge) discrepancies ideas for further improvements? apply the methods to effective center vortex model Engelhardt,Reinhardt 1999
New Mexico State University & Vienna University of Technology Thank You & Manfried Faber, Urs M. Heller, Štefan Olejník Questions?