Resonating Valence Bond Quantum Monte Carlo: Application to the ozone molecule

We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.Comment: 5 page, 3 figure

Quantum Monte Carlo Study of High Pressure Solid Molecular Hydrogen

We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {\bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {\bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules

Defects in Crystalline Packings of Twisted Filament Bundles: II. Dislocations and Grain Boundaries

Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross section and out-of-plane interfilament twist in bundles. Using non-linear continuum elasticity theory of columnar materials, we study the favorable coupling of twist-induced stresses to the presence of edge dislocations in the lattice packing of bundles, which leads to a restructuring of the ground-state order of these materials at intermediate twist. The stability of dislocations increases as both the degree of twist and lateral bundle size grow. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist, giving rise to a rich class of "polycrystalline" packings.Comment: 10 pages, 7 figure

Non-Vacuum Bianchi Types I and V in f(R) Gravity

In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.Comment: 15 pages, accepted for publication in Gen. Realtiv. Gravi

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state(E.O.S) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de-Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally couplling this ratio is -1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be $\xi<{1/4}$ >. Therefore we derive a new constraint on the value of our coupling $\xi$ . These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.Comment: 7 pages,no figures,RevTex, Typos corrected and references adde

Unconventional phase III of high-pressure solid hydrogen

We reassess the phase diagram of high-pressure solid hydrogen using mean-field and many-body wave function based approaches to determine the nature of phase III of solid hydrogen. To discover the best candidates for phase III, density functional theory calculations within the meta-generalized gradient approximation by means of the strongly constrained and appropriately normed (SCAN) semilocal density functional are employed. We study eleven molecular structures with different symmetries, which are the most competitive phases, within the pressure range of 100 to 500~GPa. The SCAN phase diagram predicts that the $C2/c-24$ and $P6_122-36$ structures are the best candidates for phase III with an energy difference of less than 1~meV/atom. To verify the stability of the competitive insulator structures of $C2/c-24$ and $P6_122-36$, we apply the diffusion Monte Carlo (DMC) method to optimise the percentage $\alpha$ of exact-exchange in the trial many-body wave function. We found that the optimised $\alpha$ equals to $40 \%$, and denote the corresponding exchange and correlation functional as PBE1. The energy gain with respect to the well-known hybrid functional PBE0, where $\alpha = 25\%$, varies with density and structure. The PBE1-DMC enthalpy-pressure phase diagram predicts that the $P6_122-36$ structure is stable up to 210~GPa, where it transforms to the $C2/c-24$. Hence, we predict that the phase III of high-pressure solid hydrogen is polymorphic.Comment: Accepted for publication in Phys. Rev.

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure $F(R)$ gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-$\Lambda$-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-$\Lambda$ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure $F(R)$ gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at $r=0$. We should note that the Kreschmann scalar of charged solutions goes to infinity as $r \rightarrow 0$, but with a rate slower than that of uncharged solutions.Comment: 21 pages, 4 figures, generalization to higher dimensions, references adde

Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid

We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC and DMC energies are obtained in the density range $1 \leq r_\text{s} \leq 40$. Single-particle and many-body finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of twist-averaged energies to the thermodynamic limit of infinite system size. System-size-dependent errors in Slater-Jastrow-backflow DMC energies caused by partially converged VMC energy minimization calculations are discussed. We find that, for $1 \leq r_\text{s} \leq 5$, optimizing the backflow function at each twist lowers the twist-averaged DMC energy at finite system size. However, nonsystematic system-size-dependent effects remain in the DMC energies, which can be partially removed by extrapolation from multiple finite system sizes to infinite system size. We attribute these nonsystematic effects to the close competition between fluid and defected crystal phases at different system sizes at low density. The DMC energies in the thermodynamic limit are used to parameterize a local spin density approximation correlation functional for inhomogeneous electron systems. Our zero-temperature phase diagram shows a single transition from a paramagnetic fluid to a hexagonal Wigner crystal at $r_\text{s}=35(1)$, with no region of stability for a ferromagnetic fluid

Equation of state of atomic solid hydrogen by stochastic many-body wave function methods

We report a numerical study of the equation of state of crystalline body-centered-cubic (BCC) hydrogen, tackled with a variety of complementary many-body wave function methods. These include continuum stochastic techniques of fixed-node diffusion and variational quantum Monte Carlo, and the Hilbert space stochastic method of full configuration-interaction quantum Monte Carlo. In addition, periodic coupled-cluster methods were also employed. Each of these methods is underpinned with different strengths and approximations, but their combination in order to perform reliable extrapolation to complete basis set and supercell size limits gives confidence in the final results. The methods were found to be in good agreement for equilibrium cell volumes for the system in the BCC phase, with a lattice parameter of 3.307 Bohr