Lattice chirality

Optimizing Chirality and Scaling of Lattice Fermions

If we construct a lattice fermion formulation, there are a number of goals to be considered: doubling should be avoided; even at finite lattice spacing a, we want to represent chiral symmetry in a sound way; and we are seeking a good scaling behavior. Conceptually we have to require locality (the lattice Dirac operator D(x, y, U) has to decay at least exponentially in |x−y| ). In addition, for ...

Lattice Chirality and Its Uses at Large N C

Path integrals are formal objects. Sometimes one says that the integration measure is ill defined, to indicate that we do know the classical action, but, as we know quite well, classical Lagrangians simply are not guaranteed to produce unique quantum mechanical systems. Separating the problem into one of measure versus one of classical action is more a psychological step than a concrete mathema...

Breaking chirality in nonequilibrium systems on the lattice

We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in the continuum and using symmetry argumen...

Lattice Chirality and the Decoupling of Mirror Fermions

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into “light” and “mirror” parts, such that the “light” and “mirror” representations are chiral. The splitting of the full partition function into “light” and “mirror” is well defined only if the two sectors are separately anomaly free. We show that only...

Anomalous Hall Effect due to the spin chirality in the Kagomé lattice