This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop ‘Perspectives in Lattice QCD’ in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and symplectic integrators; the second lecture covers topics in approximation theory and the...

After many years of research in lattice QCD, it was possible to formulate QCD with chiral fermions on the lattice [1–4]. The basic idea is an expanded flavor space which may be seen as an extra dimension with left and right handed fermions defined in the two opposite boundaries or walls. Let N be the size of the extra dimension, DW the Wilson-Dirac operator, and m the bare fermion mass. Then, t...

We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16 3 32 lattices at β = ...

We briefly review1 the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement it numerically. Finally, we give some examples of quenched calculations of chiral symmetry breaking and topology with overlap fermions. 1. Overlap formula fo...

We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux phases. For weak itineracy the flux phase is coplanar and the electronic dispersion takes the shape of graphenelike Dirac fermions. Stronger itineracy drives the formation of a noncoplanar, chiral flux phase, in which the Dirac fermions acquire a topological mas...

The magnetoresistance Rxx was investigated in arrays of abutted square cavities with lengths L ranging from 500 nm to 1.2 mm near filling factor n ­ 1y2. Maxima in Rxx occur for effective magnetic field values satisfying the magnetic focusing condition between the cavity spacing and the cyclotron radius of composite fermions, also for the effective magnetic field direction when composite fermio...

We propose that the recently observed violation of theWiedemannFranz law in the normal state of underdoped cuprates is caused by spin-charge separation and dynamical chiral symmetry breaking in a (2+1)-dimensional system consisting of massless Dirac fermions, charged bosons and a gauge field. While the d-wave spinon gap vanishes at the Fermi points, the nodal fermions acquire a finite mass due ...

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bo...

Recently the two-loop next-to-leading logarithmic (NLL) virtual corrections to arbitrary processes with massless external fermions have been calculated. Within the spontaneously broken electroweak theory the oneand two-loop mass singularities have been derived to NLL accuracy and expressed as universal correction factors depending only on the quantum numbers of the external particles. This talk...

Twoand three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids. It is shown directly that the νe = 4/11 liquid (corresponding to a ν = 1/3 filling of composite fermions in their first excite...