Singular Contractions of W-algebras

Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these exceptional values of the central charge.Comment: 10 pages, phyzzx.tex, QMW-92-7.(minor spelling and acknowledgement corrections

Kondo effect and spin quenching in high-spin molecules on metal substrates

Using a state-of-the art combination of density functional theory and impurity solver techniques we present a complete and parameter-free picture of the Kondo effect in the high-spin ($S=3/2$) coordination complex known as Manganese Phthalocyanine adsorbed on the Pb(111) surface. We calculate the correlated electronic structure and corresponding tunnel spectrum and find an asymmetric Kondo resonance, as recently observed in experiments. Contrary to previous claims, the Kondo resonance stems from only one of three possible Kondo channels with origin in the Mn 3d-orbitals, its peculiar asymmetric shape arising from the modulation of the hybridization due to strong coupling to the organic ligand. The spectral signature of the second Kondo channel is strongly suppressed as the screening occurs via the formation of a many-body singlet with the organic part of the molecule. Finally, a spin-1/2 in the 3d-shell remains completely unscreened due to the lack of hybridization of the corresponding orbital with the substrate, hence leading to a spin-3/2 underscreened Kondo effect.Comment: 5 pages, 2 figure

On the variational structure of breather solutions

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. We exemplify this idea in the case of the modified Korteweg-de Vries (mKdV), Gardner, and sine-Gordon (SG) equations. Then we perform numerical simulations that confirm, at the level of the spectral problem, our previous rigorous results, where we showed that mKdV breathers are $H^2$ and $H^1$ stable, respectively. In a second step, we also discuss the Gardner and the Sine-Gordon cases, where the spectral study of a fourth-order linear matrix system is the key element to show stability. Using numerical methods, we confirm that all spectral assumptions leading to the $H^2\times H^1$ stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. In a second part, we study the periodic mKdV case, where a periodic breather is known from the work of Kevrekidis et al. We rigorously show that these breathers satisfy a suitable elliptic equation, and we also show numerical spectral stability. However, we also identify the source of nonlinear instability in the case described in Kevrekidis et al. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.Comment: 55 pages; This paper is an improved version of our previous paper 1309.0625 and hence we replace i

A critical analysis of vacancy-induced magnetism in mono and bilayer graphene

The observation of intrinsic magnetic order in graphene and graphene-based materials relies on the formation of magnetic moments and a sufficiently strong mutual interaction. Vacancies are arguably considered the primary source of magnetic moments. Here we present an in-depth density functional theory study of the spin-resolved electronic structure of (monoatomic) vacancies in graphene and bilayer graphene. We use two different methodologies: supercell calculations with the SIESTA code and cluster-embedded calculations with the ALACANT package. Our results are conclusive: The vacancy-induced extended $\pi$ magnetic moments, which present long-range interactions and are capable of magnetic ordering, vanish at any experimentally relevant vacancy concentration. This holds for $\sigma$-bond passivated and un-passivated reconstructed vacancies, although, for the un-passivated ones, the disappearance of the $\pi$ magnetic moments is accompanied by a very large magnetic susceptibility. Only for the unlikely case of a full $\sigma$-bond passivation, preventing the reconstruction of the vacancy, a full value of 1$\mu_B$ for the $\pi$ extended magnetic moment is recovered for both mono and bilayer cases. Our results put on hold claims of vacancy-induced ferromagnetic or antiferromagnetic order in graphene-based systems, while still leaving the door open to $\sigma$-type paramagnetism.Comment: Submitted to Phys. Rev B, 9 page