Fixed point action for the massless lattice Schwinger model

Abstract

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge-invariant by considered the compact gauge transporters and localized within a $7\times 7$ lattice centered around one of the fermions. We then simulate the model at various values of $\beta$ and compare with results obtained with the Wilson fermion action. We find excellent improvement for the studied observables (propagators and masses).Comment: 17 pages (LaTeX), 6 figures (EPS); update to the published version (sorry, one year too late!

Lattice 2001: Reflections

“…The first quantitative results confirm that there are no unexpected, hidden problems with this regularization of QCD. Simulations in the Schwinger model [66] strengthen this conclusion.…”

Approximate Ginsparg–Wilson fermions: a first test

“…So far, the fixed point Dirac operator has been computed only in two dimensions [11,12,13] and it has become clear that its construction in 4-d is quite a challenging enterprise.…”

Speeding up finite step-size updating of full QCD on the lattice

“…Ref. [22] however suggests that for lattices of the size that we consider here even for full sweeps over the lattice reasonable acceptance rates are obtained when the fermion determinant is evaluated exactly. We produced almost independent configurations by updating 6400 links (which is several times the number of links of the lattice) in one proposal.…”