Phase Diagram of the One Dimensional S=1/2S=1/2 XXZXXZ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions

We have studied the phase diagram of the one dimensional $S=1/2$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points and the running of coupling constants. The second order QRG has been implemented to get the self similar Hamiltonian. This model shows a rich phase diagram which consists of different phases which possess the quantum spin-fluid and dimer phases in addition to the classical N\'{e}el and ferromagnetic ones. The border between different phases has been shown as a projection onto two different planes in the phase space

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

Leptogenesis in the presence of exact flavor symmetries

In models with flavor symmetries in the leptonic sector leptogenesis can take place in a very different way compared to the standard leptogenesis scenario. We study the generation of a $B-L$ asymmetry in these kind of models in the flavor symmetric phase pointing out that successful leptogenesis requires (i) the right-handed neutrinos to lie in different representations of the flavor group; (ii) the flavons to be lighter at least that one of the right-handed neutrino representations. When these conditions are satisfied leptogenesis proceeds due to new contributions to the CP violating asymmetry and -depending on the specific model- in several stages. We demonstrate the validity of these arguments by studying in detail the generation of the $B-L$ asymmetry in a scenario of a concrete $A_4$ flavor model realization.Comment: 25 pages, 7 figures; version 2: A few clarifications added. Version matches publication in JHE

Exact renormalization in quantum spin chains

We introduce a real-space exact renormalization group method to find exactly solvable quantum spin chains and their ground states. This method allows us to provide a complete list for exact solutions within SU(2) symmetric quantum spin chains with $S\leq 4$ and nearest-neighbor interactions, as well as examples with S=5. We obtain two classes of solutions: One of them converges to the fixed points of renormalization group and the ground states are matrix product states. Another one does not have renormalization fixed points and the ground states are partially ferromagnetic states.Comment: 8 pages, 5 figures, references added, published versio

Rigid N=2 superconformal hypermultiplets

We discuss superconformally invariant systems of hypermultiplets coupled to gauge fields associated with target-space isometries.Comment: Invited talk given at the International Seminar "Supersymmetries and Quantum Symmetries", July 1997, Dubna. Latex, 9 p

Recurrent Variational Approach to the Two-Leg Hubbard Ladder

We applied the Recurrent Variational Approach to the two-leg Hubbard ladder. At half-filling, our variational Ansatz was a generalization of the resonating valence bond state. At finite doping, hole pairs were allowed to move in the resonating valence bond background. The results obtained by the Recurrent Variational Approach were compared with results from Density Matrix Renormalization Group.Comment: 10 pages, 14 Postscript figure