Related papers: The lattice gradient flow at tree level
A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral…
We study cutoff effects at tree-level of perturbation theory for maximally twisted mass Wilson, overlap and the recently proposed Creutz fermions. We demonstrate that all three kind of lattice fermions exhibit the expected O(a^2) scaling…
Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the…
A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed…
Flavor observables are usually computed with the help of the electroweak Hamiltonian which separates the short-distance from the long-distance regime. The Wilson coefficients are calculated perturbatively, while matrix elements of the…
We compare lattice scales determined from the vector meson mass and the Wilson flow scale w_0 in QCD with two-flavours of rooted naive staggered fermions over a wide range of lattice spacing and quark mass. We find that the distributions of…
We discuss scale setting in the context of 2+1 dynamical fermion simulations where we approach the physical point in the quark mass plane keeping the average quark mass constant. We have simulations at four beta values, and after…
A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these…
The gradient flow renormalized coupling offers a simple and relatively inexpensive way to calculate the step scaling function and the lattice scale, but both applications can be hindered by large lattice artifacts. Recently we introduced an…
Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved…
We use the Wilson flow to define the gauge anisotropy at a given physical scale. We demonstrate the use of the anisotropic flow by performing the tuning of the bare gauge anisotropy in the tree-level Symanzik action for several lattice…
As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a…
We present selected preliminary lattice gauge theory results for $O(1/m_Q)$ and $O(1/m_Q^2)$ corrections to the static potential. These results are based on Wilson loops with two field strength insertions, which we renormalize using…
We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower…
We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of…
The gradient flow is a valuable tool for the lattice community, with applications from scale-setting to implementing chiral fermions. Here I focus on the gradient flow as a means to suppress power-divergent mixing. Power-divergent mixing…
We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\beta \lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator…
We show that an infinitesimal step of gradient flow can be used for defining a novel approach for computing gradients of physical observables with respect to action parameters. Compared to the commonly used perturbative expansion, this…
We give a full account of the Numerical Stochastic Perturbation Theory method for Lattice Gauge Theories. Particular relevance is given to the inclusion of dynamical fermions, which turns out to be surprisingly cheap in this context. We…
In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG $\beta$ function, an alternative…