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Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations are at the heart of our understanding of a whole novel class of phase transitions. In most of the cases, those transitions are controlled by a single type of topological objects. There are however some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realization of such cases is thus of considerable interest. We show here that this situation occurs in BaCo 2 V 2 O 8 , a spin-1/2 Ising-like quasione dimensional antiferromagnet when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological objects, which are captured by different components of the dynamical structure factor.The pioneering work of Berezinskii, Kosterlitz and Thouless (BKT) 1,2 has enlightened the role played by topological excitations in the two dimensional classical XY model. Since then, the topological aspects have been found to be crucial not only to a host of two dimensional classical systems 3 , but also in a spectacular way in the one dimensional quantum world 13 with in particular the remarkable case of spin-1 chains 5 . Such concepts have allowed to understand important aspects of the physics of materials such as the quantum hall effect 6 and even predict new classes of systems such as topological insulators 7 . Identifying and understanding the topological aspects of matter has thus become a major focus in condensed matter physics and quantum optics, where topo-logical phases such as the Haldane model 8 have been remarkably realized 9 .For classical and quantum critical phenomena, we have by now a good understanding of the prototypical topological phase transition in which only a single topological entity controls the transition. This was the case in the original BKT work, where vortex-antivortex excitations deconfine in a similar way than electrical charges in the two dimensional Coulomb gas 10 . In the quantum world, this situation is described by the celebrated sine-Gordon model, which also plays a central role in quantum field theory 11 . However, a richer and more difficult to understand class of topological transitions was rapidly pointed out to also play a major role for several systems 12,13 . This situation arises when two conjugate fields, subjected to the Heisenberg uncertainty principle and plunged into different potentials, compete with each other. The phase diagram is thus controlled by the confinement/deconfinement of the corresponding dual topological exc itations. These situations are considerably more difficult to analyse 12,13 and need much more sophisticated field theory descriptions such as the so-called dual-fie...

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We report first-principles calculations that clarify stability and electronic structures of silicene on Ag(111) surfaces. We find that several stable structures exist for silicene/Ag(111), exhibiting a variety of images of scanning tunneling microscopy. We also find that Dirac electrons are absent near Fermi level in all the stable structures due to buckling of the Si monolayer and mixing between Si and Ag orbitals. This is the first theoretical investigation that clarify the absence of Dirac electrons in silicene due to the strong interaction with substrates. We instead propose that either BN substrate or hydrogen-processed Si surface is a good candidate to preserve Dirac electrons in silicene.