Charge self-consistent dynamical mean field theory calculations incombination with linear combination of numerical atomic orbitalsframework based density functional theory

We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.

On the Generation of Davidson＇s Theory of Meaning

Established on the framework of Frege＇s philosophy of language, with the help of Tarlski in the development on the innovation oftheory of truth （including methodology level）, Davidson explained the concept of meaning in the process of language Ibrmation with the interpretation and characterization of＂the formalization of axis＂ which was Developing from ＂t refers to x＂ to ＂s means m ＂, then to＂ s means that p＂, then to ＂ （T） s is T if and only ifp＂. After a series of ideas conversion on the restructuring and improvement, Davidson finally created an innovative view of meaning on the holistic level. In order to realize the meaning of language itself as the axis, with Tarski＇s theory of truth as the transmission fulcrum, with natural language translation and interpretation as the actual operation range, he has run the theory of meaning as the understanding, interpretation and action picture of people dealing with events arranged in a crisscross pattern world.

Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory （ITP） of the dynamical mean field theory （DMFT） and coherentpotential approximation （CPA） is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tij^mn（m ≠ n） are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.

Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.

Effect of interaction and temperature on quantum phase transition in anisotropic square-octagon lattice

We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.

Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter

We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given value of qS. By use of this procedure, the scalar meson field in the Walecka＇s MFA and in Chin＇s RHA are quantized around the mean field, Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of Ф makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka＇s MFA, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin＇s RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka＇s MFA does not. We suggest to fix the parameter Ф at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory （QRMFT） a variational method.

Theoretical Study on Alpha-Decay Chains of 294 117 117 and 293 176 117

The newly synthesized element 117 and its alpha-decay chains are systematically investigated in the framework of the relativistic mean field theory with parameter sets NL-Z2 and TMA. The ground-state properties of the superheavy nuclei on the alpha-decay chains of 294 117 and 293 117 are calculated. The experimental alpha-decay energies and ha Jr-lives of the two alpha-decay chains are reasonably reproduced by the model The detailed discussions on the binding energies, alpha-decay energies, half-lives, quadrupole deformations, potential energy curves, and single particle levels of the two alpha-decay chains are made.

Fast impurity solver for dynamical mean field theory based on second order perturbation around the atomic limit

This paper proposes an impurity solver for the dynamical mean field theory （DMFT） study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA （local density approximation） ＋ DMFT studies of the Mort insulators with long range order.

Theoretical Study on N=126 Shell Evolution

The nuclei around magic number N=126 are investigated in the deformed relativistic mean field (RMF)model with effective interactions TMA.We focus investigations on the N=126 isotonic chain.The N=126 shellevolution is studied by analyzing the variations of two-neutron (proton) separation energies,quadruple deformations,single particle levels etc.The good agreement of two-neutron separation energies between experimental data and calculatedvalues is reached.The RMF theory predicts that the sizes of N=126 shell become smaller and smaller withthe increasing of proton number Z.However,the N=126 shell exists in our calculated region all along.According tothe calculated two-proton separation energies,the RMF theory suggests ^(220)Pu is a two-proton drip-line nucleus in theN=126 isotonic chain.

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random field （hi） is assumed to be Gaussian distributed with zero mean and a variance （hi2） = HRF2. The free energy （F）, the magnetization （M） and the order parameter （q） are calculated. The ferromagnetic （FM） spin-glass （SG） phase transition is clearly observed. The critical temperature （Tc） is computed under a critical intensity of random field HRF = V/2/πJ. The phase transition from FM to paramagnetic （PM） occurs at TC = J/k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility （X） shows a sharp cusp at TC and the specific heat （C） has a singularity in small random field. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulation.

Charge Densities of Unstable Nuclei with Electron Scattering

Relativistic mean-field theory and phase-shift analysis are combined together to investigate the elasticCoulomb scattering between electrons and unstable nuclei.Electron scattering at several different energies is studiedand compared,in order to see the energy dependence of electron-nucleus scattering.It is shown that electron scattering at200 MeV or 300 MeV can be used to reveal electron-nucleus scattering information around the first diffraction minimum-Shiftsin opposite directions are obtained for the first diffraction minima of the electron scattering off the ground andfirst excited states of ^(17)F with ^(16)O as reference,and similar effects are obtained for ^(18)Ne.Besides,some neutron-richN = 8 isotones are also studied.Results show that electron scattering will be very useful and important in studyingboth proton- and neutron-rich nuclei in the future.

Investigations on Nuclei near Z = 82 in Relativistic Mean Field Theory with FSUGold

In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field （RMF） theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.

New method for calculating the Berry connection in atom-molecule systems

In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.

Influence of Hyperon-Hyperon Interaction on Properties of Hadronic Star

The influences of hyperon-hyperon interaction on the overall properties of hadronic star are investigated in the framework of relativistic mean field （RMF） theory. For certain hyperon coupling, the weaker hyperon-hyperon interaction can lead to the heavier hadronic star, which accords with the observation of heavy neutron star in X-ray binaries. We find that the threshold densities of the hyperons with larger masses are brought to a lower values with the increase of the hyperon-hyperon interaction. The possibility of the existence of hyperon star is checked with the consideration of hyperon-hyperon interaction.

Effects of σ* and Φ mesons on the surface redshift of a neutron star

The effects of σ^＊ and Ф mesons on the surface redshift of a neutron star have been investigated within the framework of relativistic mean field theory for the baryon octet {n, p, ∧, ∑-,∑0, ∑＋, -, 0} system. It is found that compared with those without considering the contributions of σ^＊ and Ф mesons, the surface redshift decreases and that corresponding to the maximum value of the mass also decreases from 0.2540 to 0.2236, about by 12%. Meanwhile, it is also found that including σ^＊ and Ф mesons, the M/R and that corresponding to the maximum mass decrease.

Accurate treatments of electrostatics for computer simulations of biological systems: A brief survey of developments and existing problems

Modern computer simulations of biological systems often involve an explicit treatment of the complex interactions among a large number of molecules. While it is straightforward to compute the short-ranged Van der Waals interaction in classical molecular dynamics simulations, it has been a long-lasting issue to develop accurate methods for the longranged Coulomb interaction. In this short review, we discuss three types of methodologies for the accurate treatment of electrostatics in simulations of explicit molecules： truncation-type methods, Ewald-type methods, and mean-field-type methods. Throughout the discussion, we brief the formulations and developments of these methods, emphasize the intrinsic connections among the three types of methods, and focus on the existing problems which are often associated with the boundary conditions of electrostatics. This brief survey is summarized with a short perspective on future trends along the method developments and applications in the field of biological simulations.

A brief review of continuous models for ionic solutions: the Poisson–Boltzmann and related theories

The Poisson–Boltzmann(PB)theory is one of the most important theoretical models describing charged systems continuously.However,it suffers from neglecting ion correlations,which hinders its applicability to more general charged systems other than extremely dilute ones.Therefore,some modified versions of the PB theory are developed to effectively include ion correlations.Focused on their applications to ionic solutions,the original PB theory and its variances,including the field-theoretic approach,the correlation-enhanced PB model,the Outhwaite–Bhuiyan modified PB theory and the mean field theories,are briefly reviewed in this paper with the diagnosis of their advantages and limitations.

Density-dependent relativistic mean field approach and its application to single-Λhypernuclei in oxygen hyperisotopes

The in-medium feature of nuclear force, which includes both nucleon-nucleon( NN) and hyperon-nucleon( ΛN) interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new ΛN effective interaction in the covariant density functional(CDF) theory, namely, DD-LZ1-Λ1, is obtained by fitting the experimental data ofΛ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of Λ1p spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of theΛ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei,and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium NN interactions and core polarization effects.

Deformation constrained relativistic mean-field approach with fixed configuration and time-odd component

Deformation constrained relativistic mean-field (RMF) approach with fixed configuration and timeodd component has been developed and applied to investigate magnetic moments of light nuclei near doublyclosed shells. Taking 17O as an example, the results and discussion are given in detail.