We present a chronological review of the progress in calculating weak matrix elements using staggered fermions. We review the perturbative calculation of one-loop matching formula including both current-current diagrams and penguin diagrams using improved staggered fermions. We also present preliminary results of weak matrix elements relevant to CP violation calculated using the improved (HYP (...

The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. G...

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universalit...

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particles called 'com-posite fermions' [1–3]. The fractional quantum Hall effect [4] occurs in such a system when the ratio (or 'filling factor', ν) of the number of electrons and the degene...

Staggered Domain Wall Fermions (SDWF) combine the attractive chiral properties of staggered fermions with those of domain wall fermions. SDWF describe four flavors with exact U(1)×U(1) flavor chiral symmetry. An extra lattice dimension is introduced and the full SU(4)×SU(4) flavor chiral symmetry is recovered as its size is increased. Here, the free theory of SDWF is described and a preliminary...

A conceptual preon-based model of fermions is discussed. The preon is regarded as a topological object with three degrees of freedom in a dual three-dimensional manifold. It is shown that properties of this manifold give rise to a set of preon structures, which resemble three families of fermions. The number of preons in each structure is easily associated with the mass of a fermion. Being just...

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be in...

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry breaking. Topology-dependent ground state ...

We investigate the algebras satisfied by q-deformed boson and fermion oscillators, in particular the transformations of the algebra from one form to another. Based on a specific algebra proposed in recent literature, we show that the algebra of deformed fermions can be transformed to that of undeformed standard fermions. Furthermore we also show that the algebra of q-deformed fermions can be tr...

A model is constructed for a chiral abelian gauge-interaction of fermions and a potential of three higgses, so that the potential possesses a discrete symmetry of the vacuum state, which provides the introduction of three generations for the fermions. For the model including charged currents, a matrix of the flavor mixing is described, and a phase giving the violation of CP-invariance is determ...