Analytic formulations of the density matrix renormalization group

We present two new analytic formulations of the density matrix renormalization group (DMRG) method. In these formulations we combine the block renormalization group (BRG) procedure with the variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising model in a transverse field (ITF model) and compute several of its critical properties, which are then compared with the old BRG results.Work partially supported in part by CICYT under contracts AEN93-0776 (M.A.M.-D.) and PB92- 1092, European Community Grant ERBCHRXCT920069 (G.S.).Peer Reviewe

Dualities in spin ladders

We introduce a set of discrete modular transformations Tℓ, Uℓ and Sℓ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the two-legged ladder we show that the resonating valence bond (RVB) phase is invariant under the Sℓ transformation, while the Haldane phase is invariant under Uℓ. These two phases are related by Tℓ. Moreover, there is a 'mixed' phase, that is invariant under Tℓ, and which under Uℓ becomes the RVB phase, while under Sℓ becomes the Haldane phase. For odd ladders there exists only the Tℓ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain onto the spin 3/2 chain. Our work is based on a combination of approximate methods such as bosonization, perturbation theory and the nonlinear sigma model, adapted to the different regimes of coupling constants. 1998 IOP Publishing LtdWork partially supported by the grants NSF PHY94-07194 and the DGES (GS) and by CICYT under contract AEN93-0776 (MAM-D).Peer Reviewe

Density matrix renormalization group approach to an asymptotically free model with bound states

We apply the density matrix renormalization group (DMRG) method to the two-dimensional delta function potential which is a simple quantum mechanical model with asymptotic freedom and formation of bound states. The system block and the environment block of the DMRG contain the low energy and high energy degrees of freedom, respectively. The ground state energy and the lowest excited states are obtained with very high accuracy. We compare the DMRG method with the similarity renormalization group method and propose its generalization to field theoretical models in high energy physics. © 1999 The American Physical Society.This work was supported by the DGES Spanish Grant No. PB97-1190.Peer Reviewe

The Correlated Block Renormalization Group

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.Comment: LATEX file, 18 pages, 7 figures available upon reques

The Role of Boundary Conditions in the Real-Space Renormalization Group

We show that the failure of the real-space RG method in the 1D tight-binding model is not intrinsic to the method as considered so far but depends on the choice of boundary conditions. For fixed BC's the failure does happen. For free BC's we present a new analytical block RG-method which gives the exact ground state of the model and the correct $1/N^2$-law for the energy of the first excited state in the large $N$(size)-limit. We also give a reconstruction method for the wave-functions of the excited states.Comment: LATEX file, 12 pages, 5 figures available upon reques

Diagonal ladders: A class of models for strongly coupled electron systems

We introduce a class of models defined on ladders with a diagonal structure generated by np plaquettes. The case np=1 corresponds to the necklace ladder and has remarkable properties that are studied using density matrix renormalization-group and recurrent variational ansatzes. The antiferromagnetic Heisenberg (AFH) model on this ladder is equivalent to the alternating spin-1/spin-1/2 AFH chain, which is known to have a ferromagnetic ground state (GS). For doping 1/3 the GS is a fully doped (1,1) stripe with the holes located mostly along the principal diagonal while the minor diagonals are occupied by spin singlets. This state can be seen as a Mott insulator of localized Cooper pairs on the plaquettes. A physical picture of our results is provided by a tp-Jp-td model of plaquettes coupled diagonally with a hopping parameter td. In the limit td →∞ we recover the original t-J model on the necklace ladder while for a weak hopping parameter the model is easily solvable. The GS in the strong hopping regime is essentially an >on link> Gutzwiller projection of the weak hopping GS. We generalize the tp-Jp-td model to diagonal ladders with np≥1 and the two-dimensional square lattice. We use in our construction concepts familiar in statistical mechanics such as medial graphs and Bratelli diagrams. © 1999 The American Physical Society.G.S. and M.A.M.D. acknowledge support from the DGES under Contract No. PB96-0906, S.R.W. acknowledges support from the NSF under Grant No. DMR-9509945, D.J.S. acknowledges support from the NSF under Grant No. DMR-9527304, and J.D. acknowledges support from the DIGICYT under Contract No. PB95/0123.Peer Reviewe

Onset of microglial entry into developing quail retina coincides with increased expression of active caspase-3 and is mediated by extracellular ATP and UDP

Microglial cell precursors located in the area of the base of the pecten and the optic nerve head (BP/ONH) start to enter the retina of quail embryos at the 7 th day of incubation (E7), subsequently colonizing the entire retina by central-to-peripheral tangential migration, as previously shown by our group. The present study demonstrates a precise chronological coincidence of the onset of microglial cell entry into the retina with a striking increase in death of retinal cells, as revealed by their active caspase-3 expression and TUNEL staining, in regions dorsal to the BP/ONH area, suggesting that dying retinal cells would contribute to the microglial cell inflow into the retina. However, the molecular mechanisms involved in this inflow are currently unclear. Extracellular nucleotides, such as ATP and UDP, have previously been shown to favor migration of microglia towards brain injuries because they are released by apoptotic cells and stimulate both chemotaxis and chemokinesis in microglial cells via signaling through purinergic receptors. Hence, we tested here the hypothesis that ATP and UDP play a role in the entry and migration of microglial precursors into the developing retina. For this purpose, we used an experimental model system based on organotypic cultures of E6.5 quail embryo retina explants, which mimics the entry and migration of microglial precursors in the in situ developing retina. Inhibition of purinergic signaling by treating retina explants with either apyrase, a nucleotide-hydrolyzing enzyme, or suramin, a broad spectrum antagonist of purinergic receptors, significantly prevents the entry of microglial cells into the retina. In addition, treatment of retina explants with either exogenous ATP or UDP results in significantly increased numbers of microglial cells entering the retina. In light of these findings, we conclude that purinergic signaling by extracellular ATP and UDP is necessary for the entry and migration of microglial cells into the embryonic retina by inducing chemokinesis in these cells

Expression of Inducible Nitric Oxide Synthase (iNOS) in Microglia of the Developing Quail Retina

Inducible nitric oxide synthase (iNOS), which produce large amounts of nitric oxide (NO), is induced in macrophages and microglia in response to inflammatory mediators such as LPS and cytokines. Although iNOS is mainly expressed by microglia that become activated in different pathological and experimental situations, it was recently reported that undifferentiated amoeboid microglia can also express iNOS during normal development. The aim of this study was to investigate the pattern of iNOS expression in microglial cells during normal development and after their activation with LPS by using the quail retina as model. iNOS expression was analyzed by iNOS immunolabeling, western-blot, and RT-PCR. NO production was determined by using DAR-4M AM, a reliable fluorescent indicator of subcellular NO production by iNOS. Embryonic, postnatal, and adult in situ quail retinas were used to analyze the pattern of iNOS expression in microglial cells during normal development. iNOS expression and NO production in LPS-treated microglial cells were investigated by an in vitro approach based on organotypic cultures of E8 retinas, in which microglial cell behavior is similar to that of the in situ retina, as previously demonstrated in our laboratory. We show here that amoeboid microglia in the quail retina express iNOS during normal development. This expression is stronger in microglial cells migrating tangentially in the vitreal part of the retina and is downregulated, albeit maintained, when microglia differentiate and become ramified. LPS treatment of retina explants also induces changes in the morphology of amoeboid microglia compatible with their activation, increasing their lysosomal compartment and upregulating iNOS expression with a concomitant production of NO. Taken together, our findings demonstrate that immature microglial cells express iNOS during normal development, suggesting a certain degree of activation. Furthermore, LPS treatment induces overactivation of amoeboid microglia, resulting in a significant iNOS upregulation.This work was supported by grants from Ministerio de Economía y Competitividad, Spain (BFU2010-19981) and Junta de Andalucía, Spain (P07-CVI-03008)

Procesos de una Auditoría de Cuentas Anuales.

Un encargo de auditoría es un contrato por el que un auditor va a revisar y verificar lascuentas anuales de una entidad, con el fin de emitir un informe con su opinión. A lo largodel trabajo, observaremos todas las fases que se superan durante el proceso de unaauditoría hasta al fin emitir dicho informe. El trabajo se centra en la fase de ejecución,donde realizo una visión más práctica de distintas áreas ayudándome de los papeles detrabajo, para terminar con unas reflexiones personales a modo de conclusiones.En este trabajo he querido plasmar todos los conocimientos adquiridos durante el añoacadémico del máster, así como mi experiencia como auditor junior en una firma deauditoría.<br /