The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal $K$-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.Comment: 21 page

Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.Comment: 62 page

Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results

In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective number $N$ of edge states. We show that the fundamental commutation rules between the monodromy matrix elements are derived by solving linear systems of equations. This makes possible the construction of the transfer matrix eigenstates by means of a new recurrence relation depending on $N-1$ distinct types of creation fields. The necessary identities to solve the eigenvalue problem are obtained exploring the unitarity property and the Yang-Baxter equation satisfied by the $R$-matrix. The on-shell and off-shell properties of the algebraic Bethe ansatz are explicitly presented in terms of the arbitrary $R$-matrix elements. This includes the transfer matrix eigenvalues, the Bethe ansatz equations and the structure of the vectors not parallel to the eigenstates.Comment: 90 page

The Bethe ansatz approach for factorizable centrally extended S-matrices

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. This mapping allows us to diagonalize inhomogeneous transfer matrices whose statistical weights are given in terms of $\bf{su}(2|2)$ $S$-matrices by the algebraic Bethe ansatz. As a consequence of that we derive the quantization condition on the circle for the asymptotic momenta of particles scattering by the $\bf{su}(2|2) \otimes \bf{su}(2|2)$ $S$-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the $AdS_5 \times S^{5}$ string sigma model in the thermodynamic limit. \Comment: 22 pages, published versio

Restructuring of the "Macaronesia" biogeografic unit: a marine multi-taxon biogeographical approach

The Azores, Madeira, Selvagens, Canary Islands and Cabo Verde are commonly united under the term “Macaronesia”. This study investigates the coherency and validity of Macaronesia as a biogeographic unit using six marine groups with very different dispersal abilities: coastal fishes, echinoderms, gastropod molluscs, brachyuran decapod crustaceans, polychaete annelids, and macroalgae. We found no support for the current concept of Macaronesia as a coherent marine biogeographic unit. All marine groups studied suggest the exclusion of Cabo Verde from the remaining Macaronesian archipelagos and thus, Cabo Verde should be given the status of a biogeographic subprovince within the West African Transition province. We propose to redefine the Lusitanian biogeographical province, in which we include four ecoregions: the South European Atlantic Shelf, the Saharan Upwelling, the Azores, and a new ecoregion herein named Webbnesia, which comprises the archipelagos of Madeira, Selvagens and the Canary Islandsinfo:eu-repo/semantics/publishedVersio

A nonlinear hydrodynamical approach to granular materials

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some additional discussion. Accepted by Phys. Rev.

Stripes, Pseudogaps, and Van Hove Nesting in the Three-band tJ Model

Slave boson calculations have been carried out in the three-band tJ model for the high-T_c cuprates, with the inclusion of coupling to oxygen breathing mode phonons. Phonon-induced Van Hove nesting leads to a phase separation between a hole-doped domain and a (magnetic) domain near half filling, with long-range Coulomb forces limiting the separation to a nanoscopic scale. Strong correlation effects pin the Fermi level close to, but not precisely at the Van Hove singularity (VHS), which can enhance the tendency to phase separation. The resulting dispersions have been calculated, both in the uniform phases and in the phase separated regime. In the latter case, distinctly different dispersions are found for large, random domains and for regular (static) striped arrays, and a hypothetical form is presented for dynamic striped arrays. The doping dependence of the latter is found to provide an excellent description of photoemission and thermodynamic experiments on pseudogap formation in underdoped cuprates. In particular, the multiplicity of observed gaps is explained as a combination of flux phase plus charge density wave (CDW) gaps along with a superconducting gap. The largest gap is associated with VHS nesting. The apparent smooth evolution of this gap with doping masks a crossover from CDW-like effects near optimal doping to magnetic effects (flux phase) near half filling. A crossover from large Fermi surface to hole pockets with increased underdoping is found. In the weakly overdoped regime, the CDW undergoes a quantum phase transition ($T_{CDW}\to 0$), which could be obscured by phase separation.Comment: 15 pages, Latex, 18 PS figures Corrects a sign error: major changes, esp. in Sect. 3, Figs 1-4,6 replace