Showing papers on "Random phase approximation published in 2010"
TL;DR: In this paper, lattice constants, bulk moduli, and atomization energies of solids using the correlation energy evaluated within the adiabatic connection fluctuation-dissipation framework and applying the random-phase approximation are presented.
Abstract: We present lattice constants, bulk moduli, and atomization energies of solids using the correlation energy evaluated within the adiabatic connection fluctuation-dissipation framework and applying the random-phase approximation. Recently, we have shown [Phys. Rev. Lett. 103, 056401 (2009)] that geometrical properties and heats of formation are well described within this approximation. We extend this study to a larger set of materials and focus on the treatment of metals and the effect introduced by the frozen-core approximation.
368 citations
TL;DR: The structural properties of graphite, such as the interlayer equilibrium distance, the elastic constant, and the net layer binding energy, are obtained using the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation.
Abstract: The structural properties of graphite, such as the interlayer equilibrium distance, the elastic constant, and the net layer binding energy, are obtained using the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation. Excellent agreement is found with the available experimental data; however, our computed binding energy of 48 meV per atom is somewhat smaller than the one obtained by quantum Monte Carlo methods. The asymptotic behavior of the interlayer dispersion interaction, previously derived from analytic approximations, is explicitly demonstrated to follow a ${d}^{\ensuremath{-}3}$ behavior at very large distances.
345 citations
TL;DR: The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.
Abstract: The random phase approximation (RPA) is an increasingly popular post-Kohn–Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Moller–Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations an...
237 citations
TL;DR: In this paper, the relationship between the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonance was investigated by using different random phase approximation (RPA) models based on a representative set of Skyrme effective forces plus meson exchange effective Lagrangians.
Abstract: Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonance (PDR) in $^{68}\mathrm{Ni}$ and $^{132}\mathrm{Sn}$ are investigated by using different random phase approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.
201 citations
TL;DR: This work shows that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation, and presents a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second- order screened exchange correlation.
Abstract: There has been considerable recent interest in density functionals incorporating random phase approximation (RPA) ground-state correlation. By virtue of its full nonlocality, RPA correlation is compatible with exact Hartree-Fock-type exchange and describes van der Waals interactions exceptionally well [B. G. Janesko et al., J. Chem. Phys. 130, 081105 (2009); J. Chem. Phys. 131, 034110 (2009)]. One caveat is that RPA correlation contains one-electron self-interaction error, which leads to disturbingly large correlation energies in the stretched bond situation of, e.g., H(2)(+), He(2)(+), or Ne(2)(+). In the present work, we show that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation. We present a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second-order screened exchange correlation. This correction has a generally small, and sometimes undesirable, effect on RPA predictions for chemical properties, but appears to be very beneficial for the dissociation of H(2)(+), He(2)(+), and Ne(2)(+).
141 citations
TL;DR: In this paper, the random phase approximation (RPA) correlation energy is expressed in terms of the exact local Kohn-Sham (KS) exchange potential and corresponding adiabatic and nonadiabatic exchange kernels for density-functional reference determinants.
Abstract: The random phase approximation (RPA) correlation energy is expressed in terms of the exact local Kohn–Sham (KS) exchange potential and corresponding adiabatic and nonadiabatic exchange kernels for density-functional reference determinants. The approach naturally extends the RPA method in which, conventionally, only the Coulomb kernel is included. By comparison with the coupled cluster singles doubles with perturbative triples method it is shown for a set of small molecules that the new RPA method based on KS exchange yields correlation energies more accurate than RPA on the basis of Hartree–Fock exchange.
125 citations
TL;DR: In this paper, the role of hole pocket at the (π, π) point of the unfolded Brillouin zone, identified as crucial to the pairing by Kuroki et al. is discussed.
Abstract: Experiments on the iron–pnictide superconductors appear to show some materials where the ground state is fully gapped, and others where low-energy excitations dominate, possibly indicative of gap nodes. Within the framework of a five-orbital spin fluctuation theory for these systems, we discuss how changes in the doping, the electronic structure or interaction parameters can tune the system from a fully gapped to a nodal sign-changing gap with s-wave (A1g) symmetry (s±). In particular, we focus on the role of the hole pocket at the (π, π) point of the unfolded Brillouin zone, identified as crucial to the pairing by Kuroki et al (2009 Phys. Rev. B 79 224511), and show that its presence leads to additional nesting of hole and electron pockets, which stabilizes the isotropic s± state. The pocket's contribution to the pairing can be tuned by doping, surface effects and by changes in interaction parameters, which we examine. Analytic expressions for orbital pairing vertices calculated within the random phase approximation (RPA) fluctuation exchange approximation allow us to draw connections between aspects of the electronic structure, interaction parameters and the form of the superconducting gap.
88 citations
TL;DR: In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments, and sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmettrizedIntegrals in others.
Abstract: The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.
87 citations
TL;DR: In this article, a connection between static correlation and self-interaction from the perspective provided by the random phase approximation is made, and the connection between the two concepts is discussed.
Abstract: Semi-local density functional theory suggests a connection between static correlation and self-interaction. It is difficult to make such a connection from the wave function theory perspective, since few wave function methods permit self-interaction error. However, the random phase approximation for ground-state correlation, which has a wave function derivation, does include self-interaction in its direct (Hartree) variant. This variant also describes left–right correlation. The self-interaction can be removed by means of second-order screened exchange; however, this also has negative consequences for the description of static correlation. This paper discusses the connection between the two concepts (static correlation and self-interaction) from the perspective provided by the random phase approximation.
86 citations
TL;DR: In this paper, the binding energy (BE) curves of rare gas and alkaline-earth dimers using an energy functional that includes exact exchange (EXX) and correlation energies within the random phase approximation (RPA) were studied.
Abstract: We present a study of the binding energy (BE) curves of rare gas and alkaline-earth dimers using an energy functional that includes exact exchange (EXX) and correlation energies within the random phase approximation (RPA). Our results for the equilibrium positions and long range behavior of the potential energy curves show great improvements over those obtained at the density functional theory level, within local and semilocal approximations. BEs are improved as well in the case of rare gas dimers. For Ar and Kr, the accuracy of our results is comparable to that of so-called van der Waals density functionals, although EXX/RPA yields BE curves that agree better with experiment for large separation distances, as expected. We also discuss shortcomings of the EXX/RPA perturbative approach and analyze possible sources of error in the description of the potential energy curve of alkaline-earth dimers, in particular, Be2, exhibiting an unphysical maximum at large separations. We suggest that the lack of self-con...
80 citations
TL;DR: While the proper correction to RPA is short-ranged in some systems, its contribution to the correlation hole can spread out in a molecule with multiple atomic centers, canceling part of the spread of the exact exchange hole, making the true exchange-correlation hole more localized than in RPA or RPA+.
Abstract: There is current interest in the random phase approximation (RPA), a "fifth-rung" density functional for the exchange-correlation energy. RPA has full exact exchange and constructs the correlation with the help of the unoccupied Kohn-Sham orbitals. In many cases (uniform electron gas, jellium surface, and free atom), the correction to RPA is a short-ranged effect that is captured by a local spin density approximation (LSDA) or a generalized gradient approximation (GGA). Nonempirical density functionals for the correction to RPA were constructed earlier at the LSDA and GGA levels (RPA+), but they are constructed here at the fully nonlocal level (RPA++), using the van der Waals density functional (vdW-DF) of Langreth, Lundqvist, and collaborators. While they make important and helpful corrections to RPA total and ionization energies of free atoms, they correct the RPA atomization energies of molecules by only about 1 kcal/mol. Thus, it is puzzling that RPA atomization energies are, on average, about 10 kcal/mol lower than those of accurate values from experiment. We find here that a hybrid of 50% Perdew-Burke-Ernzerhof GGA with 50% RPA+ yields atomization energies much more accurate than either one does alone. This suggests a solution to the puzzle: While the proper correction to RPA is short-ranged in some systems, its contribution to the correlation hole can spread out in a molecule with multiple atomic centers, canceling part of the spread of the exact exchange hole (more so than in RPA or RPA+), making the true exchange-correlation hole more localized than in RPA or RPA+. This effect is not captured even by the vdW-DF nonlocality, but it requires the different kind of full nonlocality present in a hybrid functional.
Abstract: We discuss calculations of the single-particle states in magic nuclei, performed within the particle-vibration coupling (PVC) approach by using consistently the Skyrme effective interaction. The vibrations are calculated within fully self-consistent random-phase approximation and the whole interaction is also used in the PVC vertex. Our main emphasis is therefore the discussion of our results in comparison with those in which some approximation is made. The perspectives for improving current density functional theory (DFT) calculations are also addressed.
TL;DR: In this article, the vibrational and rotational collective masses (inertial functions) are determined by local normal modes built on constrained Hartree-Fock-Bogoliubov states and numerical calculations are carried out using the pairing-plus-quadrupole Hamiltonian including the quadrupole-pairing interaction within the two major-shell active model spaces both for neutrons and protons.
Abstract: On the basis of the adiabatic self-consistent collective coordinate method, we develop an efficient microscopic method of deriving the five-dimensional quadrupole collective Hamiltonian and illustrate its usefulness by applying it to the oblate-prolate shape coexistence/mixing phenomena in proton-rich $^{68,70,72}\mathrm{Se}$. In this method, the vibrational and rotational collective masses (inertial functions) are determined by local normal modes built on constrained Hartree-Fock-Bogoliubov states. Numerical calculations are carried out using the pairing-plus-quadrupole Hamiltonian including the quadrupole-pairing interaction within the two major-shell active model spaces both for neutrons and protons. It is shown that the time-odd components of the moving mean-field significantly increase the vibrational and rotational collective masses in comparison with the Inglis-Belyaev cranking masses. Solving the collective Schr\"odinger equation, we evaluate excitation spectra, quadrupole transitions, and moments. The results of the numerical calculation are in excellent agreement with recent experimental data and indicate that the low-lying states of these nuclei are characterized as an intermediate situation between the oblate-prolate shape coexistence and the so-called $\ensuremath{\gamma}$ unstable situation where large-amplitude triaxial-shape fluctuations play a dominant role.
TL;DR: It is found that the EXX/RPA perturbative approach provides an overall satisfactory, first-principles description of dispersion forces, but binding energies tend to be underestimated, and possible reasons for this discrepancy are discussed.
Abstract: We investigated intermolecular interactions in weakly bonded molecular assemblies from first principles, by combining exact exchange energies (EXX) with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the random phase approximation (RPA). We considered three different types of molecular systems: the benzene crystal, the methane crystal, and self-assembled monolayers of phenylenediisocyanide, which involve aromatic rings, sp(3)-hybridized C-H bonds, and isocyanide triple bonds, respectively. We describe in detail how computed equilibrium lattice constants and cohesive energies may be affected by the input ground state wave functions and orbital energies, by the geometries of molecular monomers in the assemblies, and by the inclusion of zero-point energy contribution to the total energy. We find that the EXX/RPA perturbative approach provides an overall satisfactory, first-principles description of dispersion forces. However, binding energies tend to be underestimated, and possible reasons for this discrepancy are discussed.
TL;DR: It is shown that the use of the second-order expansion of the RPA correlation energy results in rather inaccurate binding energy curves for weakly bonded systems, and the accuracy of different exchange energy functionals used in the derivation of vdW density functionals is assessed.
Abstract: We derive a power expansion of the correlation energy of weakly bound systems within the random phase approximation (RPA), in terms of the Coulomb interaction operator, and we show that the asymptotic limit of the second- and third-order terms yields the van der Waals (vdW) dispersion energy terms derived by Zaremba–Kohn and Axilrod–Teller within perturbation theory. We then show that the use of the second-order expansion of the RPA correlation energy results in rather inaccurate binding energy curves for weakly bonded systems, and discuss the implications of our findings for the development of approximate vdW density functionals. We also assess the accuracy of different exchange energy functionals used in the derivation of vdW density functionals.
TL;DR: In this paper, the results of neutron-scattering and angle-resolved photoemission experiments for the Fe-pnictide parent compounds, and their metallic nature, are shown to impose severe constraints on the range of values that can be considered ''realistic'' for the intraorbital Hubbard repulsion $U$ and Hund coupling $J$ in multiorbital Hubbard models treated in the mean-field approximation.
Abstract: The results of neutron-scattering and angle-resolved photoemission experiments for the Fe-pnictide parent compounds, and their metallic nature, are shown to impose severe constraints on the range of values that can be considered ``realistic'' for the intraorbital Hubbard repulsion $U$ and Hund coupling $J$ in multiorbital Hubbard models treated in the mean-field approximation. Phase diagrams for three- and five-orbital models are here provided, and the physically realistic regime of couplings is highlighted, to guide future theoretical work into the proper region of parameters of Hubbard models. In addition, using the random phase approximation, the pairing tendencies in these realistic coupling regions are investigated. It is shown that the dominant spin-singlet pairing channels in these coupling regimes correspond to nodal superconductivity, with strong competition between several states that belong to different irreducible representations. This is compatible with experimental bulk measurements that have reported the existence of nodes in several Fe-pnictide compounds.
TL;DR: In this paper, the second RPA (SRPA) calculations of nuclear response are performed and analyzed, where the ground state and residual couplings are described by the same Hamiltonian and no arbitrary truncations are imposed on the model space.
Abstract: Second RPA (SRPA) calculations of nuclear response are performed and analyzed. Unlike in most other SRPA applications, the ground state, approximated by the Hartree-Fock (HF) ground state, and the residual couplings are described by the same Hamiltonian and no arbitrary truncations are imposed on the model space. Finite-range interactions are used and thus divergence problems are not present. We employ a realistic interaction, derived from the Argonne V18 potential using the unitary correlation operator method (UCOM), as well as the simple Brink-Boeker interaction. Representative results are discussed, mainly on giant resonances and low-lying collective states. The focus of the present work is not on the comparison with data, but rather on technical and physical aspects of the method. We present how the large-scale eigenvalue problem that SRPA entails can be treated, and demonstrate how the method operates in producing self-energy corrections and fragmentation. The so-called diagonal approximation is conditionally validated. Stability problems are traced back to missing ground-state correlations.
TL;DR: In this paper, the second random-phase approximation (RPA) with a Skyrme force is performed to describe both high and low-lying excited states in {sup 16}O. The coupling between one particle-one hole and two particle-two hole configurations among themselves is fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered.
Abstract: Second random-phase approximation (RPA) calculations with a Skyrme force are performed to describe both high- and low-lying excited states in {sup 16}O. The coupling between one particle-one hole and two particle-two hole as well as that between two particle-two hole configurations among themselves are fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond the standard RPA will be considered in detail in a forthcoming paper. Two approximations are employed here for these rearrangement terms: they are either neglected or evaluated with the RPA procedure. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by the second RPA owing to the huge number of two particle-two hole configurations. A better description of the excitation energies of the low-lying 0{sup +} and 2{sup +} states is obtained with the second RPA than with the RPA.
TL;DR: In this paper, the same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels.
Abstract: We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self-consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed $^{24--26}\mathrm{Mg}$, $^{34}\mathrm{Mg}$ isotopes are presented and compared to experimental findings.
TL;DR: An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers.
Abstract: An algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and x-ray spectroscopies. An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the C(6) coefficients of Rb(2) and Cs(2) are equal to 14.0x10(3) and 21.9x10(3) a.u., respectively.
TL;DR: In this paper, the temperature-dependent charge carrier transport of bilayer graphene (BLG) impacted by Coulomb impurity scattering within the random phase approximation is calculated and the polarizability is equal to the density of states at zero momentum transfer and is enhanced by a factor of log{4}$ at large momentum transfer for arbitrary temperature.
Abstract: We calculate the temperature-dependent charge carrier transport of bilayer graphene (BLG) impacted by Coulomb impurity scattering within the random phase approximation. We find the polarizability is equal to the density of states at zero momentum transfer and is enhanced by a factor $\log{4}$ at large momentum transfer for arbitrary temperature. The sharp cusp of static polarizability at $q=2k_F$, due to the strong backward scattering, would be smooth by the increasing temperatures. We also obtain the asymptotic behaviors of conductivity of BLG at low and high temperature, and find it turns from a two dimensional electron gas (2DEG) like linear temperature metallic behavior to a single layer graphene (SLG) like quadratic temperature insulating behavior as the temperature increases.
TL;DR: In this article, the single impurity problem in iron-pnictide superconductors is investigated by solving the Bogoliubov-de Gennes (BdG) equation in a microscopic multiorbital model.
Abstract: The single-impurity problem in iron-pnictide superconductors is investigated by solving the Bogoliubov–de Gennes (BdG) equation in a microscopic multiorbital model. We construct a five-orbital model suitable for the BdG analysis, which reproduces the results of random phase approximation in a uniform case. Using this model, we study the local density of states around a nonmagnetic impurity and discuss the bound-state peak structure, which can be used for distinguishing the s +- and s ++ states. A bound state with nearly zero energy is found in the case of the impurity potential I ∼1.0 eV, while the bound-state peaks stick to the gap edge in the unitary limit | I |→∞. A novel multiple-peak structure originating from the multiorbital nature of iron pnictides is also found.
TL;DR: In this article, an implementation of a new method to calculate random phase approximation (RPA) strength functions with iterative non-Hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix was reported.
Abstract: We report on an implementation of a new method to calculate random phase approximation (RPA) strength functions with iterative non-Hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus $^{132}\mathrm{Sn}$ and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.
TL;DR: In this article, a quasi-particle random phase approximation (QRPA) for neutrino scattering off even-even nuclei via neutral current (NC) and charged cur- rent (CC) is proposed.
Abstract: We developed the quasi-particle random phase approximation (QRPA) for the neutrino scattering off even-even nuclei via neutral current (NC) and charged cur- rent (CC). The QRPA has been successfully applied for the \beta and \beta\beta decay of relevant nuclei. To describe neutrino scattering, general multipole transitions by weak interactions with a finite momentum transfer are calculated for NC and CC reaction with detailed formalism. Since we consider neutron-proton (np) pairing as well as neutron-neutron (nn) and proton-proton (pp) pairing correlations, the nn + pp QRPA and np QRPA are combined in a framework, which enables to describe both NC and CC reactions in a consistent way. Numerical results for
u-^{12}C, -^{56}Fe and -^{56}Ni reactions are shown to comply with other theoretical calculations and reproduce well available experimental data.
TL;DR: In this paper, the authors studied the effect of inelastic proton scattering on the population of the first 2+ state of 74Ni with the objective of quantifying the de-excitation cross section.
TL;DR: This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome, and is applied to the determination of the proton stopping power.
Abstract: In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.
TL;DR: The role played by the anharmonicities on the calculations of the vibrational corrections has also been analyzed and the obtained results indicate that the an-harmonic terms are important for the dc-Pockels and dc-Kerr effects as mentioned in this paper.
Abstract: In this work we present the results for hyperpolarizabilities of the methanol molecule including vibrational corrections and electron correlation effects at the CCSD level. Comparisons to random phase approximation results previously reported show that the electron correlation is in general important for both electronic contribution and vibrational corrections. The role played by the anharmonicities on the calculations of the vibrational corrections has also been analyzed and the obtained results indicate that the anharmonic terms are important for the dc-Pockels and dc-Kerr effects. For the other nonlinear optical properties studied the double-harmonic approximation is found to be suitable. Comparison to available experimental result in gas phase for the dc-second harmonic generation second hyperpolarizability shows a very good agreement with the electronic contribution calculated here while our total value is 14% larger than the experimental value.
TL;DR: A strong signature of the hybridization between graphene's pi plasmon and the substrate's phonon is found in both the HREELS spectra and the stopping force, which reveals the importance of phonon excitations in an insulating substrate.
Abstract: We provide a theoretical model that describes the dielectric coupling of a two-dimensional (2D) layer of graphene, represented by a polarization function in the random phase approximation, and a semi-infinite three-dimensional (3D) substrate, represented by a surface response function in a non-local formulation. We concentrate on the role of the dynamic response of the substrate for low-frequency excitations of the combined graphene–substrate system, which give rise to the stopping force on slowly moving charges above doped graphene. A comparison of the dielectric loss function with experimental high-resolution electron energy loss spectroscopy (HREELS) data for graphene on a SiC substrate is used to estimate the effects of damping rate and the local field correction in graphene, as well as to reveal the importance of phonon excitations in an insulating substrate. While the local field correction and linearly dispersing damping rate did not yield any important effects compared to the constant damping rate in graphene, a strong signature of the hybridization between graphene's π plasmon and the substrate's phonon is found in both the HREELS spectra and the stopping force. A friction coefficient that is calculated for slow charges moving above graphene on a metallic substrate shows an interplay between the low-energy single-particle excitations in both systems.
TL;DR: In this article, the authors obtained the complete phase diagram of the hard-core Bose-Hubbard model in the presence of a period-two superlattice in two and three dimensions.
Abstract: We obtain the complete phase diagram of the hard-core Bose-Hubbard model in the presence of a period-two superlattice in two and three dimensions. First we acquire the phase boundaries between the superfluid phase and the ``trivial'' insulating phases of the model (the completely-empty and completely-filled lattices) analytically. Next, the boundary between the superfluid phase and the half-filled Mott-insulating phase is obtained numerically, using the stochastic series expansion algorithm followed by finite-size scaling. We also compare our numerical results against the predictions of several approximation schemes, including two mean-field approaches and a fourth-order strong-coupling expansion, where we show that the latter method in particular is successful in producing an accurate picture of the phase diagram. Finally, we examine the extent to which several approximation schemes, such as the random phase approximation and the strong-coupling expansion, give an accurate description of the momentum distribution of the bosons inside the insulating phases.