We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10 %. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.
Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-$k$ Chern-Simons action, ``half-CS" term and the mixed Chern-Simons (BF) coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, …
Recently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories on the basis of a chiral overlap operator. We compute the classical continuum limit of the fermion number anomaly in this formulation. Unexpectedly, we find that the continuum limit contains a term which is not Lorentz invariant. The term is, however, proportional to the gauge anomaly coefficient, and thus the fermion number anomaly in this lattice formulation automatically restores the Lorentz-invariant form when and only when the anomaly cancellation condition is met.
We present first results of classical-statistical real-time simulations of anomalous transport phenomena with overlap fermions. We find that even on small lattices overlap fermions reproduce the real-time anomaly equation with much better precision than Wilson-Dirac fermions on an order of magnitude larger lattices. The difference becomes much more pronounced for quickly changing electromagnetic fields, especially if one takes into account the back-reaction of fermions on electromagnetism. As test cases, we consider chirality pumping in parallel electric and magnetic fields and mixing between …
狄拉克算子对向量的作用通常通过多移位共轭梯度求解器间接实现。所需的计算时间取决于用作重叠核的矩阵的条件数$κ$。虽然Wilson动作通常用作重叠核，但FLIC（Fat Link Irrelevant Clover）动作具有改进的条件数，并且在评估重叠动作时提供高达两倍的加速。本文综述了FLIC重叠费米子研究的最新进展。
Numerical experiences are reported with overlap fermions which employ the Brillouin action as a kernel. After discussing the dispersion relations of both the kernel and the resulting chiral action, some of the physics features are addressed on quenched backgrounds. We find that the overlap with Brillouin kernel is much better localized than the overlap with Wilson kernel. Also a preliminary account is given of the cost of the formulation, in terms of CPU time and memory.
