Related papers: Multigrid for Staggered Lattice Fermions
The worldsheet formulation is introduced for lattice gauge theories with dynamical fermions. The partition function of lattice compact QED with staggered fermions is expressed as a sum over surfaces with border on self-avoiding fermionic…
A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field…
We have studied $O(a^2)$ improved lattice QCD with the staggered fermion by using Symanzik's program. We find that there are 5 dimension-6 fermion bilinears and gauge operators. In addition, there are 10 four-fermion operators which are…
A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion…
In order to develop fast inversion algorithms we have used overlap solvers in two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional space-times dimensions has always been a testing ground for algorithms. By the…
In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of…
We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…
We show how a path integral for reduced K\"{a}hler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level integration scheme. The quark propagator is expanded in series of terms with a well defined hierarchical…
We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities…
Quasiparticle excitations beyond Dirac-Weyl-Majorana classification can appear in lattice systems due to the less symmetry constraint compared with Poincar\'e symmetry in high energy physics. In particular, fermions with an integer spin can…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
In this talk, I will give an overview of the theoretical status of staggered Lattice QCD with the "fourth-root trick." In this regularization of QCD, a separate staggered quark field is used for each physical flavor, and the inherent…
In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…
We construct a fermion system in a multi-kink-antikink soliton background, and present in an explicit form all its trapped configurations (bound state solutions) as well as scattering states. This is achieved by exploiting an exotic N=4…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
We consider three improvements to seed methods for Hermitian linear systems with multiple right-hand sides: only the Krylov subspace for the first system is used for seeding subsequent right-hand sides, the first right-hand side is solved…
A different lattice fermion method is introduced. Staggered domain wall fermions are defined in 2n+1 dimensions and describe 2^n flavors of light lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As the size of the…
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces…