We analyze topological objects in pure gluonic SU(2) lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological charge. On a 12 × 4 lattice it turns out that topological quantities have a non-trivial local correlation. The auto-correlation functions of the topological char...

The purpose of this paper is to show that an isomorphism between the lattices of all closed sets of two topological spaces induces an isomorphism on the lattices of their zero-sets. This is achieved by showing that any continuous real-valued function on a space X can be transferred to any space latticeequivalent to X. Several topological properties are shown to be lattice-invariant.

We report a direct observation of surface dominated conduction in an intrinsic Bi(2)Se(3) thin film with a thickness of six quintuple layers grown on lattice-matched CdS (0001) substrates by molecular beam epitaxy. Shubnikov-de Haas oscillations from the topological surface states suggest that the Fermi level falls inside the bulk band gap and is 53 ± 5 meV above the Dirac point, which is in ag...

The recently developed families index theory for the overlap lattice Dirac operator is applied to demonstrate an interplay between topological features of the space of SU(N) lattice gauge fields on the 4-torus and the existence question for G0 gauge fixings which do not have the Gribov problem. The continuum version of our considerations leads to topological obstructions to the existence of suc...

We study the renormalization group evolution up to the xed point of the lattice topological susceptibility in the 2{d O(3) non{linear {model. We start with a discretization of the continuum topological charge by a local charge density, polynomial in the lattice elds. Among the diierent choices we propose also a Symanzik{improved lattice topological charge. We check step by step in the renormali...

We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along t...

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant an...

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configur...

The low–energy excited states of a system of interacting one–dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called “Luttinger liquid”) are characterized by the velocities uρ and uσ of the charge and spin excitations, as well as by a parameter Kρ that determines the power law behavior of correlatio...

The spin1 2 Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition, where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition ~rather than the character of the electronic states changing from insulati...