Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.Comment: Accepted for publication in Physical Review

Group-wise penalized estimation schemes in model-based clustering

Gaussian mixture models provide a probabilistically sound clustering approach. However, their tendency to be over-parameterized endangers their utility in high dimensions. To induce sparsity, penalized model-based clustering strategies have been explored. Some of these approaches, exploiting the link between Gaussian graphical models and mixtures, allow to handle large precision matrices, encoding variables relationships. By assuming similar components sparsity levels, these methods fall short when the dependence structures are group-dependent. Our proposal, by penalizing group-specific transformations of the precision matrices, automatically handles situations where under or over-connectivity between variables is witnessed. The performances of the method are shown via a real data experimen

Penalized Model-Based Clustering with Group-Dependent Shrinkage Estimation

Gaussian mixture models (GMM) are the most-widely employed approach to perform model-based clustering of continuous features. Grievously, with the increasing availability of high-dimensional datasets, their direct applicability is put at stake: GMMs suffer from the curse of dimensionality issue, as the number of parameters grows quadratically with the number of variables. To this extent, a methodological link between Gaussian mixtures and Gaussian graphical models has recently been established in order to provide a framework for performing penalized model-based clustering in presence of large precision matrices. Notwithstanding, current methodologies do not account for the fact that groups may be under or over-connected, thus implicitly assuming similar levels of sparsity across clusters. We overcome this limitation by defining data-driven and component specific penalty factors, automatically accounting for different degrees of connections within groups. A real data experiment on handwritten digits recognition showcases the validity of our proposal

Magnetic field dependence of charge stripe order in La2-xBaxCuO4 (x~1/8)

We have carried out a detailed investigation of the magnetic field dependence of charge ordering in La2-xBaxCuO4 (x~1/8) utilizing high-resolution x-ray scattering. We find that the charge order correlation length increases as the magnetic field greater than ~5T is applied in the superconducting phase (T=2K). The observed unusual field dependence of the charge order correlation length suggests that the static charge stripe order competes with the superconducting ground state in this sample.Comment: 4 pages, 4 figure

Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the Boltzmann constant

We report on a new optical implementation of primary gas thermometry based on laser absorption spectrometry in the near infrared. The method consists in retrieving the Doppler broadening from highly accurate observations of the line shape of the R(12) $\nu_{1} + 2 \nu_{2}^{\phantom{1}0} + \nu_{3}$ transition in CO$_{2}$ gas at thermodynamic equilibrium. Doppler width measurements as a function of gas temperature, ranging between the triple point of water and the gallium melting point, allowed for a spectroscopic determination of the Boltzmann constant with a relative accuracy of $\sim1.6\times10^{-4}$.Comment: Submitted to Physical Review Letter

Angular dependence of the magnetization of isotropic superconductors: which is the vortex direction?

We present studies of the dc magnetization of thin platelike samples of the isotropic type II superconductor PbTl(10%), as a function of the angle between the normal to the sample and the applied magnetic field ${\bf H}$. We determine the magnetization vector ${\bf M}$ by measuring the components both parallel and normal to ${\bf H}$ in a SQUID magnetometer, and we further decompose it in its reversible and irreversible contributions. The behavior of the reversible magnetization is well understood in terms of minimization of the free energy taking into account geometrical effects. In the mixed state at low fields, the dominant effect is the line energy gained by shortening the vortices, thus the flux lines are almost normal to the sample surface. Due to the geometrical constrain, the irreversible magnetization ${\bf M}_{irr}$ remains locked to the sample normal over a wide range of fields and orientations, as already known. We show that in order to undestand the angle and field dependence of the modulus of ${\bf M}_{irr}$, which is a measure of the vortex pinning, and to correctly extract the field dependent critical current density, the knowledge of the modulus and orientation of the induction field ${\bf B}$ is required.Comment: 11 pages, 6 figure

Persistent X-Ray Photoconductivity and Percolation of Metallic Clusters in Charge-Ordered Manganites

Charge-ordered manganites of composition $\rm Pr_{1-x}(Ca_{1-y}Sr_{y})_{x}MnO_3$ exhibit persistent photoconductivity upon exposure to x-rays. This is not always accompanied by a significant increase in the {\it number} of conduction electrons as predicted by conventional models of persistent photoconductivity. An analysis of the x-ray diffraction patterns and current-voltage characteristics shows that x-ray illumination results in a microscopically phase separated state in which charge-ordered insulating regions provide barriers against charge transport between metallic clusters. The dominant effect of x-ray illumination is to enhance the electron {\it mobility} by lowering or removing these barriers. A mechanism based on magnetic degrees of freedom is proposed.Comment: 8 pages, 4 figure

Equilibrium tuned by a magnetic field in phase separated manganite

We present magnetic and transport measurements on La5/8-yPryCa3/8MnO3 with y = 0.3, a manganite compound exhibiting intrinsic multiphase coexistence of sub-micrometric ferromagnetic and antiferromagnetic charge ordered regions. Time relaxation effects between 60 and 120K, and the obtained magnetic and resistive viscosities, unveils the dynamic nature of the phase separated state. An experimental procedure based on the derivative of the time relaxation after the application and removal of a magnetic field enables the determination of the otherwise unreachable equilibrium state of the phase separated system. With this procedure the equilibrium phase fraction for zero field as a function of temperature is obtained. The presented results allow a correlation between the distance of the system to the equilibrium state and its relaxation behavior.Comment: 13 pages, 5 figures. Submited to Journal of Physics: Condensed Matte

Properties of charge density waves in La2−x_{2-x}Bax_{x}CuO4_4

We report a comprehensive x-ray scattering study of charge density wave (stripe) ordering in $\rm La_{2-x}Ba_xCuO_4 (x \approx 1/8)$, for which the superconducting $T_c$ is greatly suppressed. Strong superlattice reflections corresponding to static ordering of charge stripes were observed in this sample. The structural modulation at the lowest temperature was deduced based on the intensity of over 70 unique superlattice positions surveyed. We found that the charge order in this sample is described with one-dimensional charge density waves, which have incommensurate wave-vectors (0.23, 0, 0.5) and (0, 0.23, 0.5) respectively on neighboring $\rm CuO_2$ planes. The structural modulation due to the charge density wave order is simply sinusoidal, and no higher harmonics were observed. Just below the structural transition temperature, short-range charge density wave correlation appears, which develops into a large scale charge ordering around 40 K, close to the spin density wave ordering temperature. However, this charge ordering fails to grow into a true long range order, and its correlation length saturates at $\sim 230\AA$, and slightly decreases below about 15 K, which may be due to the onset of two-dimensional superconductivity.Comment: 11 pages, 9 figure