We construct a new perfect action for free staggered fermions, which is more local than the one obtained from the standard block average scheme. This pays off in superior properties after a short ranged truncation. This action is "gauged by hand" and tested in Schwinger model simulations by means of a new variant of hybrid MC. Using "fat links" for the gauge field, we obtain a tiny "pion" mass down to β < ∼ 1.5, and the "eta" mass follows very closely the prediction of asymptotic scaling.It has been observed that a good implementation of classically perfect actions provides an excellent level of improvement in the sense that lattice artifacts are drastically suppressed. However, the most successful applications have been limited to two dimensions so far, and they involve a huge number of couplings [1,2]. This implies that corresponding 4d actions are hardly applicable. Therefore it is crucial to achieve good improvement with rather few extra terms, and also this can be studied first in d = 2. However, the known classically perfect actions of Refs. [1,2] are not local enough for a very short ranged truncation to be sensible, hence -in view of d = 4 -different construction methods should be considered. Here we present a successful application of "gauging by hand", i.e. we use the truncated perfect couplings of the free fermion and insert gauge couplings by hand. This leads to a relatively modest overhead in the number of couplings compared to the standard action, but to an improvement on the same level as classical perfection. We conclude that this procedure is promising for d = 4. order to preserve the remnant chiral symmetry U (1) ⊗ U (1). This can be achieved by blocking each flavor separately [3]. As an improvement over the standard block average (BA) scheme [4], we propose "partial decimation" (PD) [5]. The free propagator ∆ BA is built by averaging source and sink in each block, whereas in the PD scheme one only averages the source and treats the sink by decimation, or vice versa. Both lead to local perfect actions for free staggered fermions, and in both cases we optimize the locality by tuning the RGT parameters. The optimization criterion is that the mapping down to d = 1, ∆ −1 (p 1 , 0, . . . , 0), only couples nearest neighbors. For the PD scheme this is the case for a simple δ function blocking at m = 0 [5]. However, that criterion can be fulfilled at arbitrary mass m. In d > 1 the PD scheme leads to a superior degree of locality, i.e. to a faster exponential decay of the couplings. Hence the truncation can be expected to be less harmful.The truncation itself should also be done with some care. We found mixed periodic boundary conditions to be optimal: we impose antiperiodicity over 6 lattice spacings in the direction of odd coupling distance, and periodicity over 6 lattice spacings in the other direction(s). The resulting couplings in d = 2 are given in the following Table; for d = 4 we refer again to Ref. [5]. There we also discuss massive fermions, including the case of non-degenerated flavors.
We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.
The perfect action of free staggered fermions is calculated by blocking from the continuum for degenerate and non-degenerate flavor masses. The symmetry structure, connecting flavor transformations and translations, is explained directly from the blocking scheme. It is convenient to use a modified Fourier transformation, respecting this connection, to treat the spin-flavor structure of the blockspins. The perfect action remains local in the non-degenerate case; it is explicitly calculated in two dimensions. I finally comment on the relation of the blocking scheme to the transition from Dirac-K\"ahler fermions to staggered fermions.Comment: 14 pages, Latex2e, 1 Latex figure, some minor changes and two references adde
We compare continuum and lattice formulation of the geometric Schwinger Model on the torus. The lattice reproduces the U(1)A anomaly, related to non-trivial topological gauge con gurations and zero modes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.