Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite

In Volborthite, spin-1/2 moments form a distorted Kagom\'e lattice, of corner sharing isosceles triangles with exchange constants $J$ on two bonds and $J'$ on the third bond. We study the properties of such spin systems, and show that despite the distortion, the lattice retains a great deal of frustration. Although sub-extensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern. In the low temperature limit, an effective chirality Hamiltonian is derived from non-linear spin waves which predicts a transition on increasing $J'/J$, from $\sqrt 3\times \sqrt 3$ type order to a new ferrimagnetic {\em striped chirality} order with a doubled unit cell. This is confirmed by a large-N approximation on the O($n$) model on this lattice. While the saddle point solution produces a line degeneracy, $O(1/n)$ corrections select the non-trivial wavevector of the striped chirality state. The quantum limit of spin 1/2 on this lattice is studied via exact small system diagonalization and compare well with experimental results at intermediate temperatures. We suggest that the very low temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.Comment: revised, section V about exact diagonalization is extensively rewritten, 17 pages, 11 figures, RevTex 4, accepted by Phys. Rev.

Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb2O7

A recent study [Tassel {\it et al.}, Phys. Rev. Lett. {\bf 105}, 167205 (2010)] has proposed a remarkable spin model for (CuCl)LaNb2O7, in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intra-dimer exchange coupling J>0 is antiferromagnetic, while the inter-dimer exchange couplings are ferromagnetic and take different values, J_x,J_y<0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb2O7 and related compounds, we theoretically investigate the ground state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small J_x and J_y, exact diagonalization for finite clusters, and a Schwinger boson mean field theory. When |J_x|, |J_y| <~ J, the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit J_x=J_y=0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the inter-dimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |J_x| or |J_y| >~ J, quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb2O7 and related compounds are discussed in light of our theoretical results and existing experimental data.Comment: 21 pages, 20 figure

The dissimilar chemical composition of the planet-hosting stars of the XO-2 binary system

Using high-quality spectra of the twin stars in the XO-2 binary system, we have detected significant differences in the chemical composition of their photospheres. The differences correlate strongly with the elements' dust condensation temperature. In XO-2N, volatiles are enhanced by about 0.015 dex and refractories are overabundant by up to 0.090 dex. On average, our error bar in relative abundance is 0.012 dex. We present an early metal-depletion scenario in which the formation of the gas giant planets known to exist around these stars is responsible for a 0.015 dex offset in the abundances of all elements while 20 M_Earth of non-detected rocky objects that formed around XO-2S explain the additional refractory-element difference. An alternative explanation involves the late accretion of at least 20 M_Earth of planet-like material by XO-2N, allegedly as a result of the migration of the hot Jupiter detected around that star. Dust cleansing by a nearby hot star as well as age or Galactic birthplace effects can be ruled out as valid explanations for this phenomenon.Comment: ApJ, in press. Complete linelist (Table 3) available in the "Other formats -> Source" downloa

Biocompatible Mesoporous Hollow Carbon Nanocapsules for High Performance Supercapacitors.

A facile and general method for the controllable synthesis of N-doped hollow mesoporous carbon nanocapsules (NHCNCs) with four different geometries has been developed. The spheres (NHCNC-1), low-concaves (NHCNC-2), semi-concaves (NHCNC-3) and wrinkles (NHCNC-4) shaped samples were prepared and systematically investigated to understand the structural effects of hollow particles on their supercapacitor performances. Compared with the other three different shaped samples (NHCNC-1, NHCNC-2, and NHCNC-4), the as-synthesized semi-concave structured NHCNC-3 demonstrated excellent performance with high gravimetric capacitance of 326 F g-1 (419 F cm-3) and ultra-stable cycling stability (96.6% after 5000 cycles). The outstanding performances achieved are attributed to the unique semi-concave structure, high specific surface area (1400 m2 g-1), hierarchical porosity, high packing density (1.41 g cm-3) and high nitrogen (N) content (up to 3.73%) of the new materials. These carbon nanocapsules with tailorable structures and properties enable them as outstanding carriers and platforms for various emerging applications, such as nanoscale chemical reactors, catalysis, batteries, solar energy harvest, gas storage and so on. In addition, these novel carbons have negligible cytotoxicity and high biocompatibility for human cells, promising a wide range of bio applications, such as biomaterials, drug delivery, biomedicine, biotherapy and bioelectronic devices

A note on modular forms and generalized anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formula

Path integrals and symmetry breaking for optimal control theory

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schr\"odinger equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. It is shown, how in the deterministic limit the PMP formalism is recovered. The significance of the path integral approach is that it forms the basis for a number of efficient computational methods, such as MC sampling, the Laplace approximation and the variational approximation. We show the effectiveness of the first two methods in number of examples. Examples are given that show the qualitative difference between stochastic and deterministic control and the occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA

The detailed chemical composition of the terrestrial planet host Kepler-10

Chemical abundance studies of the Sun and solar twins have demonstrated that the solar composition of refractory elements is depleted when compared to volatile elements, which could be due to the formation of terrestrial planets. In order to further examine this scenario, we conducted a line-by-line differential chemical abundance analysis of the terrestrial planet host Kepler-10 and fourteen of its stellar twins. Stellar parameters and elemental abundances of Kepler-10 and its stellar twins were obtained with very high precision using a strictly differential analysis of high quality CFHT, HET and Magellan spectra. When compared to the majority of thick disc twins, Kepler-10 shows a depletion in the refractory elements relative to the volatile elements, which could be due to the formation of terrestrial planets in the Kepler-10 system. The average abundance pattern corresponds to ~ 13 Earth masses, while the two known planets in Kepler-10 system have a combined ~ 20 Earth masses. For two of the eight thick disc twins, however, no depletion patterns are found. Although our results demonstrate that several factors (e.g., planet signature, stellar age, stellar birth location and Galactic chemical evolution) could lead to or affect abundance trends with condensation temperature, we find that the trends give further support for the planetary signature hypothesis.Comment: 12 pages, 11 figures, accepted for publication in MNRA