We study the dual Higgs mechanism for the nonperturbative QCD. We point out two kind of the “seesaw” relations between electric and magnetic sectors. Owing to the Dirac condition eg = 4π, the dual Ginzburg-Landau theory has the asymptotic freedom nature on the gauge coupling constant e, where the “walking coupling constant” is predicted for e in the infrared region. We study also QCD-monopoles ...

Throughout the last decades of lattice QCD topological excitations have played a crucial and sometimes controversial role. It is natural, in particular in view of the purpose of this volume in honor of Adriano Di Giacomo, that they are a topic also here.1 The topological charge of a gauge configuration is a well-defined concept only in the continuum and for differentiable fields. In quantum fie...

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics ...

We consider a recent proposal by Horváth et al. to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dira...

Scaling and topology in the 2–d O(3) σ–model on the lattice with the fixed point action Abstract We study scaling properties and topological aspects of the 2–d O(3) non–linear σ–model on the lattice with the parametrized fixed point action recently proposed by P. Hasenfratz and F. Niedermayer. The behavior of the mass gap confirms the good properties of scaling of the fixed point action. Concer...

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge ac...

We propose to observe and manipulate topological edge spins in a one-dimensional optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservatio...

Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

Graphene, made of sp^{2} hybridized carbon, is characterized with a Dirac band, representative of its underlying 2D hexagonal lattice. The fundamental understanding of graphene has recently spurred a surge in the search for 2D topological quantum phases in solid-state materials. Here, we propose a new form of 2D material, consisting of sd^{2} hybridized transition metal atoms in hexagonal latti...