Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules

We present a new class of tensor network states that are specifically designed to capture the electron correlation of a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spin for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm

Accurate ab initio spin densities

We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys. 2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insights into chemically interesting features of the molecule under study such as the distribution of $\alpha$- and $\beta$-electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure

Hysteresis of spectral evolution in the soft state of black-hole binary LMC X-3

We report the discovery of hysteresis between the x-ray spectrum and luminosity of black-hole binary LMC X-3. Our observations, with the Proportional Counter Array on the Rossi X-ray Timing Explorer, took place entirely within the soft spectral state, dominated by a spectral component that was fitted well with a multicolor disk blackbody. A power-law component was seen only during times when the luminosity of the disk blackbody was declining. The x-ray luminosity at these times was comparable to that seen in transient systems (x-ray novae) when they return to the hard state at the end of an outburst. Our observations may represent partial transitions to the hard state; complete transitions have been seen in this system by Wilms et al. (2001). If they are related to the soft-to-hard transition in transients, then they demonstrate that hysteresis effects can appear without a full state transition. We discuss these observations in the context of earlier observations of hysteresis within the hard state of binaries 1E 1740.7-2942 and GRS 1758-258 and in relation to published explanations of hysteresis in transients.Comment: 14 pages, 6 figures, accepted by The Astrophysical Journa

Quantum information analysis of electronic states at different molecular structures

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization. We also discuss the application of the configuration interaction based dynamically extended active space procedure which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures to a great extent. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal orbital ordering and carry out efficient calculations on transition metal clusters. We propose a recipe to perform DMRG calculations in a black-box fashion and we point out the connections of our work to other tensor network state approaches

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.Comment: 14 pages, 4 figure

Strut-and-tie model based on crack band theory for deep beams

yesA simplified strut-and-tie model including size effect based on the crack band theory is proposed to evaluate the shear capacity of deep beams. Concrete struts are idealized as uniformly tapered prismatic members with a stress relief strip whereas horizontal and vertical shear reinforcements are assumed to be an internally statically indeterminate system. The shear transfer mechanism of concrete and shear reinforcement is then driven by using the energy equilibrium in the stress relief strip and crack band zone of concrete struts. The shear capacity predictions of deep beams obtained from the present models are in better agreement with 637 test results than those determined from strut-and-tie models proposed by ACI 318-08, EC-2, and Tan and Cheng. In addition, the trend of the shear capacity of deep beams against different parameters as predicted by the present models has a consistent agreement with that observed from experimental results. In particular, the present model shows that the normalized shear capacity of deep beams is proportional to (h)−0.25, where h = section overall depth

Possible scale invariant linear magnetoresistance in pyrochlore iridates Bi2Ir2O7

We report the observation of a linear magnetoresistance in single crystals and epitaxial thin films of the pyrochlore iridate Bi2Ir2O7. The linear magnetoresistance is positive and isotropic at low temperatures, without any sign of saturation up to 35 T. As temperature increases, the linear field dependence gradually evolves to a quadratic field dependence. The temperature and field dependence of magnetoresistance of Bi2Ir2O7 bears strikingly resemblance to the scale invariant magnetoresistance observed in the strange metal phase in high Tc cuprates. However, the residual resistivity of Bi2Ir2O7 is more than two orders of magnitude higher than the curpates. Our results suggest that the correlation between linear magnetoresistance and quantum fluctuations may exist beyond high temperature superconductors

On the Calibration of Full-polarization 86GHz Global VLBI Observations

We report the development of a semi-automatic pipeline for the calibration of 86 GHz full-polarization observations performed with the Global Millimeter-VLBI array (GMVA) and describe the calibration strategy followed in the data reduction. Our calibration pipeline involves non-standard procedures, since VLBI polarimetry at frequencies above 43 GHz is not yet well established. We also present, for the first time, a full-polarization global-VLBI image at 86 GHz (source 3C 345), as an example of the final product of our calibration pipeline, and discuss the effect of instrumental limitations on the fidelity of the polarization images. Our calibration strategy is not exclusive for the GMVA, and could be applied on other VLBI arrays at millimeter wavelengths. The use of this pipeline will allow GMVA observers to get fully-calibrated datasets shortly after the data correlation.Comment: 10 pages, 10 figures. Accepted for publication in A&

Eddington-limited X-ray Bursts as Distance Indicators. I. Systematic Trends and Spherical Symmetry in Bursts from 4U 1728-34

We investigate the limitations of thermonuclear X-ray bursts as a distance indicator for the weakly-magnetized accreting neutron star 4U 1728-34. We measured the unabsorbed peak flux of 81 bursts in public data from the Rossi X-Ray Timing Explorer (RXTE). The distribution of peak fluxes was bimodal: 66 bursts exhibited photospheric radius expansion and were distributed about a mean bolometric flux of 9.2e-8 erg/cm^2/s, while the remaining (non-radius expansion) bursts reached 4.5e-8 erg/cm^2/s, on average. The peak fluxes of the radius-expansion bursts were not constant, exhibiting a standard deviation of 9.4% and a total variation of 46%. These bursts showed significant correlations between their peak flux and the X-ray colors of the persistent emission immediately prior to the burst. We also found evidence for quasi-periodic variation of the peak fluxes of radius-expansion bursts, with a time scale of approximately 40 d. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasi-periodic variability on a similar time scale. We suggest that these variations may have a common origin in reflection from a warped accretion disk. Once the systematic variation of the peak burst fluxes is subtracted, the residual scatter is only approximately 3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that i) the radiation from the neutron star atmosphere during radius-expansion episodes is nearly spherically symmetric, and ii) the radius-expansion bursts reach a common peak flux which may be interpreted as a standard candle intensity.Adopting the minimum peak flux for the radius-expansion bursts as the Eddington flux limit, we derive a distance for the source of 4.4-4.8 kpc.Comment: 9 pages, 7 figures, accepted by ApJ. Minor referee's revisions, also includes 9 newly public X-ray burst