Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field

Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ that gives the power-law decay of the oscillations of the $\alpha-$Renyi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger parameter $K$, as proposed by Calabrese et al. [Phys. Rev. Lett. 104, 095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was also observed for some non-zero values of the magnetization $m$. We show that for $s>1/2$ the amplitudes of the oscillations are quite small, and get accurate estimates of $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ become a challenge. Although our estimates of the new universal exponents $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.Comment: revised version, accepted to PRB. 9 pages, 3 Figures, 4 Table

Coexistence of Pairing Tendencies and Ferromagnetism in a Doped Two-Orbital Hubbard Model on Two-Leg Ladders

Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state.For the electronic density $\rho=2$, i.e. the undoped limit, our investigations show a robust $(\pi,0)$ antiferromagnetic ground state, as in previous investigations. Doping away from $\rho=2$ and for large values of the Hund coupling $J$, a ferromagnetic region is found to be stable. Moreover, when the interorbital on-site Hubbard repulsion is smaller than the Hund coupling, i.e. for $U'<J$ in the standard notation of multiorbital Hubbard models, our results indicate the coexistence of pairing tendencies and ferromagnetism close to $\rho=2$. These results are compatible with previous investigations using one dimensional systems. Although further research is needed to clarify if the range of couplings used here is of relevance for real materials, such as superconducting heavy fermions or pnictides, our theoretical results address a possible mechanism for pairing that may be active in the presence of short-range ferromagnetic fluctuations.Comment: 8 pages, 4 Fig

Minimum Length from Quantum Mechanics and Classical General Relativity

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a {\it device independent} limit on possible position measurements.Comment: 8 pages, latex, to appear in the Physical Review Letter

Quantum anisotropic Heisenberg chains with superlattice structure: a DMRG study

Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-1/2 XXZ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a non trivial plateau with the magnetization value given by the relative sizes of the sub-chains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.Comment: 6 pages, 6 figure

Los riesgos geológicos en la Ordenación Territorial

There are wide areas of the planet where the incidence of natural catastrophes is very high, particularly in areas with high population density or where areas under natural risks are occupied. Most of these areas belong to a clear tectonic setting.In addition, public awareness on these natural catastrophic phenomenon acquires nowadays an additional dimension due to the important role of mass media. Mass media informs immediately al1 over the world on these caastrophes, for example, the big earthquakes (Mexico, California, Japan), landslides, floods, eruptions, hurricanes, etc.These geological phenomena are caused by the normal processes within the earth's crust, which have social and economic consequences. These processes have shaped our planet,with more or less dramatic consequences depending on their speed and intensity.Catastrophic events are gauged by their environmental effects, mainly on the biosphere. Socioeconomic disasters have also augmented as the increase and concentration of population have increased the risk on populated areas.Finally, the necessity of preventive measures is clear on global risks, such as the effects of global warming of those resulting from the management of water resources.

Detection of gravitational waves from the QCD phase transition with pulsar timing arrays

If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.Comment: 7 pages, 5 figs. Version accepted by PR

Inspiraling Halo Accretion Mapped in Lyman-α\alpha Emission around a z∼3z\sim3 Quasar

In an effort to search for Ly$\alpha$ emission from circum- and intergalactic gas on scales of hundreds of kpc around $z\sim3$ quasars, and thus characterise the physical properties of the gas in emission, we have initiated an extensive fast-survey with the Multi Unit Spectroscopic Explorer (MUSE): Quasar Snapshot Observations with MUse: Search for Extended Ultraviolet eMission (QSO MUSEUM). In this work, we report the discovery of an enormous Ly$\alpha$ nebula (ELAN) around the quasar SDSS~J102009.99+104002.7 at $z=3.164$, which we followed-up with deeper MUSE observations. This ELAN spans $\sim297$ projected kpc, has an average Ly$\alpha$ surface brightness ${\rm SB}_{\rm Ly\alpha}\sim 6.04\times10^{-18}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$ (within the $2\sigma$ isophote), and is associated with an additional four, previously unknown embedded sources: two Ly$\alpha$ emitters and two faint active galactic nuclei (one Type-1 and one Type-2 quasar). By mapping at high significance the line-of-sight velocity in the entirety of the observed structure, we unveiled a large-scale coherent rotation-like pattern spanning $\sim300$ km s$^{-1}$ with a velocity dispersion of $<270$ km s$^{-1}$, which we interpret as a signature of the inspiraling accretion of substructures within the quasar's host halo. Future multiwavelength data will complement our MUSE observations, and are definitely needed to fully characterise such a complex system. None the less, our observations reveal the potential of new sensitive integral-field spectrographs to characterise the dynamical state of diffuse gas on large scales in the young Universe, and thereby witness the assembly of galaxies.Comment: 39 pages with 27 figures and 5 appendices. Accepted to MNRA

Identification of molecular species of simple lipids by normal phase liquid chromatography-positive electrospray tandem mass spectrometry, and application of developed methods in comprehensive analysis of low erucic acid rapeseed oil lipids

Mono-, di- and triacylglycerol (MAG, DAG, TAG), sterol ester (SE), free sterol (S) and free fatty acid (FFA) standards were analyzed in the presence of ammonium ions and ammonia by flow injection MS2 and MS3, and by normal phase-liquid chromatography (NP-LC) MS2 positive electrospray ionization (ESI) mass spectrometry (MS). The MS data recorded for ammonium adducts ([M+NH4]+) of TAGs, DAGs, and MAGs were consistent with stepwise fragmentation mechanisms. In the first step, ammonium ion in [M+NH4]+ donates proton to acylglycerol and ammonia is released. In the second step, FFA is cleaved from protonated TAG, water from protonated 1,3-DAG and MAG, both FFA and water from protonated 1,2-DAG, hence leading to formation of [DAG]+ ion from TAG and 1,3-DAG, [DAG]+ and [MAG]+ ions from 1,2-DAG, and [MAG]+ ion from MAG. In the third step, [DAG]+ ion of TAG is fragmented to yield [Acyl]+, [Acyl + 74]+, [DAG−74]+ ions, [DAG] ion of 1,3-DAG to [Acyl]+ ions, and [MAG]+ ion of MAG to protonated FAs, which are decomposed to water and [Acyl]+ ions in the fourth step. A stepwise mechanism for fragmentation of FFA was also evident from MS2 and MS3 data. Molecular species of low erucic acid rapeseed oil simple lipids were identified from characteristic ions produced in the NP-LC–ESI-MS2 of [M+NH4]+ ions. The percentage composition of the molecular species of each lipid class was calculated from integrated extracted ion chromatograms of [(M+NH4)]+ ions of SE, TAG,MAG, and FFA, of the sum of [(M+NH4)]+ and [(M+NH4)−NH3 −H2O]+ ions of both regioisomers of DAGs, and of sterol fragment ions of S

Vortex distribution in the Lowest Landau Level

We study the vortex distribution of the wave functions minimizing the Gross Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level (LLL): we prove that the minimizer cannot have a finite number of zeroes thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of ``invisible'' vortices: the distortion of the lattice is very small in the Thomas Fermi region but quite large outside, where the "invisible" vortices lie.Comment: 4 pages, 1 figur