相关论文: Weyl and ghost fermions on the lattice

In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…

The recent discovery of the Lorentz symmetry-violating 'Type II' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed matter systems. However, tuning the exceptional properties of this novel state has remained…

We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around…

Motivated by recent examples of three-dimensional lattice Hamiltonians with massless Dirac fermions in their (bulk) spectrum, I revisit the problem of fermion doubling on bipartite lattices. The number of components of the Dirac fermion in…

The recent discovery of Weyl fermions in solids enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. They are constituted of pairs of Weyl points with two-fold band degeneracy, which…

We consider the fermion spectrum in the strong coupling vortex phase of a lattice fermion-scalar model with a global $U(1)_L\times U(1)_R$, in 2D, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers…

It is well known that a quantized two-dimensional Weyl fermion coupled to gravity spoils general covariance and breaks the covariant conservation of the energy-momentum tensor. In this brief article, we point out that the quantum…

We work the lattice fermions and non-Hermitian formulation in the 2D GNY model and demonstrate the numerical implementation for two flavors by the Hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a…

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…

For a simple-cubic optical lattice with lattice spacing d, occupied by two species of fermionic atoms of mass m that interact repulsively, we ask what conditions maximize the Neel temperature in the Mott insulating phase at density one atom…

Weyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of `Weyl nodes'. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in $3+1$…

Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on…

I discretize axion string configuration coupled to a Dirac fermion, which in the continuum binds a massless chiral fermion in its core when the winding is one. I show that such a configuration can host one or more chiral fermions when…

In spite of the breakthrough in non-perturbative chiral gauge theories during the last decade, the present formulation has stubborn artefacts. Independently of the fermion representation one is confronted with unwanted CP violation and…

We give a pedagogical review of implications of chiral symmetry in QCD. First, we briefly discuss classical textbook subjects such as the axial anomaly, spontaneous breaking of the flavor-nonsinglet chiral symmetry, formation of light…

We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking…

The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for the naive discretization of a single (massless) Dirac cone on a two-dimensional surface. The inevitable appearance of an additional, unphysical fermionic mode can,…

In the present work we analyse $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of $\mathcal{N}=1$ SYM theory in four dimensions. As in…

We consider the ($3{+}1$)-dimensional Maxwell theory in the situation where going around nontrivial paths in the spacetime involves the action of the duality transformation exchanging the electric field and the magnetic field, as well as…

We study the effects of strong $1/r$ long-range Coulomb interactions in a Weyl semimetal. We consider a three-dimensional (3D) Dirac fermion system on a lattice with a time-reversal symmetry breaking term, and take into account $1/r$…