Modified DMRG algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J2/J1J_2/J_1

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange $J_1$, $J_2$ between first and second neighbors. The modified algorithm yields accurate results up to $J_2/J_1 \approx 4$ for the magnetic gap $\Delta$ to the lowest triplet state, the amplitude $B$ of the bond order wave (BOW) phase, the wavelength $\lambda$ of the spiral phase, and the spin correlation length $\xi$. The $J_2/J_1$ dependences of $\Delta$, $B$, $\lambda$ and $\xi$ provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.Comment: 7 pages, 8 figures, submitted to PR

Dynamic response studies on aggregation and breakage dynamics of colloidal dispersions in stirred tanks

Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks using small-angle static light scattering. It was found that the steady-state values of the root-mean-square radius of gyration are fully reversible upon changes of stirring speed as well as solid volume fraction. Steady-state values of the root-mean-square radius of gyration were decreasing with decreasing solid volume fraction as well as with increasing stirring speed. Moreover, it was found that the steady-state structure and shape of the aggregates is not influenced by the applied stirring speed

Magnetic susceptibility of alkali-TCNQ salts and extended Hubbard models with bond order and charge density wave phases

The molar spin susceptibilities $\chi(T)$ of Na-TCNQ, K-TCNQ and Rb-TCNQ(II) are fit quantitatively to 450 K in terms of half-filled bands of three one-dimensional Hubbard models with extended interactions using exact results for finite systems. All three models have bond order wave (BOW) and charge density wave (CDW) phases with boundary $V = V_c(U)$ for nearest-neighbor interaction $V$ and on-site repulsion $U$. At high $T$, all three salts have regular stacks of $\rm TCNQ^-$ anion radicals. The $\chi(T)$ fits place Na and K in the CDW phase and Rb(II) in the BOW phase with $V \approx V_c$. The Na and K salts have dimerized stacks at $T < T_d$ while Rb(II) has regular stacks at 100K. The $\chi(T)$ analysis extends to dimerized stacks and to dimerization fluctuations in Rb(II). The three models yield consistent values of $U$, $V$ and transfer integrals $t$ for closely related $\rm TCNQ^-$ stacks. Model parameters based on $\chi(T)$ are smaller than those from optical data that in turn are considerably reduced by electronic polarization from quantum chemical calculation of $U$, $V$ and $t$ on adjacent $\rm TCNQ^-$ ions. The $\chi(T)$ analysis shows that fully relaxed states have reduced model parameters compared to optical or vibration spectra of dimerized or regular $\rm TCNQ^-$ stacks.Comment: 9 pages and 5 figure

Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition

We present exact diagonalization results on a modified Peierls-Hubbard model for the neutral-ionic phase transition. The ground state potential energy surface and the infrared intensity of the Peierls mode point to a strong, non-linear electron-phonon coupling, with effects that are dominated by the proximity to the electronic instability rather than by electronic correlations. The huge infrared intensity of the Peierls mode at the ferroelectric transition is related to the temperature dependence of the dielectric constant of mixed-stack organic crystals.Comment: 4 pages, 4 figure

Global Waste Management Outlook

The Global Waste Management Outlook, a collective effort of the United Nations Environment Programme and the International Waste Management Association, is a pioneering scientific global assessment on the state of waste management and a call for action to the international community. Prepared as a follow up to the Rio+20 Summit and as a response to UNEP Governing Council decision GC 27/12, the document establishes the rationale and the tools for taking a holistic approach towards waste management and recognizing waste and resource management as a significant contributor to sustainable development and climate change mitigation. To complement the Sustainable Development Goals of the Post-2015 Development Agenda, the Outlook sets forth Global Waste Management Goals and a Global Call to Action to achieve those goals

Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on a Square Lattice

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated for several possible dimerized configurations, some of which are shown to have lower ground state energies than the others. In particular, the lattice deformations resulting in alternate stronger and weaker couplings along both the principal axes of a square lattice are shown to result in a larger gain in magnetic energy. In addition, a `columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a `staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and energy gap, which is qualitatively different from that reported earlier. Instead of increasing as $\delta ^{x}$, the two quantities depend on $\delta$ as $\delta ^{\nu}/| \ln \delta | .$ This is true both in the near critical regime $(0\leq \delta \leq 0.1)$ as well as in the far regime $(0\leq \delta <1)$. It is suggested that the unexpanded exchange coupling is as much a source of the logarithmic dependence as a correction due to the contribution of umklapp processes. Staggered magnetization is shown to follow the same $\delta$-dependence in all the configurations in the small $\delta$-regime, while for $0\leq \delta <1$, it follows the power law $\delta ^{x}$.Comment: 12 pages, 7 Postscript figures, RevTex forma

On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms