Related papers: An Approximate Large $N$ Method for Lattice Chiral…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an…
The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a…
While chiral quantum field theories (QFTs) describe a wide range of physical systems, from the standard model to topological quantum matter, the realization of chiral QFTs on a lattice has proved to be difficult due to the Nielsen-Ninomiya…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent…
We construct large-N_c motivated approximate chiral SU(3) amplitudes of next-to-next-to-leading order. The amplitudes are independent of the renormalization scale. Fitting lattice data with those amplitudes allows for the extraction of…
A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically…
We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear sigma-model contains, at the lowest level, an additional term with two derivatives.…
The large-$N$ limit of $O(N)$-symmetric bosonic field theories, or $U(N)$-symmetric fermionic field theories, is amenable to a saddle point approximation. As a result, there is a family of closely related algorithms for efficient lattice…
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of $N=2$ lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious chiral fermion…
We discuss the critical behaviour of strongly interacting matter close to the QCD phase transition. Emphasis is put on a presentation of results from lattice calculations that illustrate deconfining as well as chiral symmetry restoring…
In this paper, we obtain the analytical solutions of two kinds of transcendental equations with numerous applications in college physics by means of Lagrange inversion theorem, and rewrite them in the form of ratio of rational polynomials…
We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null…
We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories…
The Schwinger model is studied in a finite lattice by means of the P-representation. The vacuum energy, mass gap and chiral condensate are evaluated showing good agreement with the expected values in the continuum limit.
We introduce a new approximation to nucleon matrix determinants that is physically motivated by chiral effective theory. The method involves breaking the lattice into spatial zones and expanding the determinant in powers of the boundary…
We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. For non-compact and Wilson formulation of the gauge field action…
We study the Yukawa model on a 4-dimensional Euclidean lattice in the quenched approximation. A particular attention is given to the singularities of the Dirac operator in the phase diagram. A careful analysis of a particular limiting case…
We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or…