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.

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.

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.

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.

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）.

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.

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48. Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square （rms） radii of charge and neutron, and shell gaps have been calculated. The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42. The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43. The evolution of shell gaps with proton number Z can be clearly observed. Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region. In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.

Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory

Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self- consistent relativistic mean field （RMF） model with the pairing correlations treated by a shell-mode-like approach （SLAP）, in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF＋SLAP calculations.

Moments of inertia of neutron stars in relativistic mean field theory:The role of the isovector scalar channel

With the inclusion of the isovector scalar channel in the meson-nucleon couplings, taking DD-MEδ as an effective interaction, the moments of inertia of neutron stars possessing various stellar masses are studied within the density dependent relativistic mean field （RMF） theory. The isovector scalar channel contributes to the softening of the neutron-star matter equation of state （EOS） and therefore the reduction of the maximum mass and radius of neutron stars. Smaller values of the total moment of inertia 1 and the crustal moment of inertia AI are then obtained in DD-ME~ via numerical procedure in comparison with those in other selected RMF functionals. In addition, the involvement of the isovector scalar channel lowers the thickness of the neutron star crust and its mass fi＇action as well. The sensitivity to both the crustal mass and stellar radius causes the crustal moment of inertia to be more obviously reduced than the total one, eventually leading to a suppression on the fraction of crustal moment of inertia △I/I in DD-MFδ. The results indicate the crustal moment of inertia as a more sensitive probe of the neutron-star matter EOS than the total one, and demonstrate that the isovector scalar meson-nucleon couplings in the RMF theory could exert influence over the physics of pulsar glitches.

A systematic study of the superdeformation of Pb isotopes with relativistic mean field theory

The microscopically constrained relativistic mean field theory is used to investigate the superdeformation for Pb isotopes. The calculations have been performed with the four different interactions NL3, PK1, TM1 and NLSH, and show that there exists a clear superdeformed minimum in the potential energy surfaces. The excitation energy, deformation and depth of the well in the superdef.ormed minimum are comparable for the four different interactions. Furthermore the trend for the change of the superdeformed excitation energy with neutron number is correctly reproduced. The calculated two-neutron separation energy in the ground state and superdeformed minimum together with their differences are in agreement with the available data. The larger energy difference appearing in the superdeformed minimum reflects a lower average level density at superdeformations for Pb isotopes.

A New Determination of the Lambda-Nucleon Coupling Constants in Relativistic Mean Field Theory

A new determination of the Lambda-nucleon coupling constants in relativistic mean field theory is presented by optimizing both hyperon binding energy and spin-orbit splitting, ttypernuclear single particle spectra with the new coupling constants suggest the good agreement between the calculation and available data. The spin-orbit splitting of hyperon in medium mass hypernuclei is systematically larger than that in light- or heavy-mass hypernuclei. The sensitivity of the Lambda spin-orbit splitting to the omega-Lambda-Laznbda tensor coupling term is also explored.

Towards Lambda-nucleon coupling constants in relativistic mean field theory

New parameter sets for Λ-nucleon coupling in relativistic mean field theory are proposed based on nucleon-nucleon effective interaction PK1. Hypernuclear properties are described well through a systematical study. Effects of hyperon tensor coupling term on spin-orbit splitting are also investigated self-consistently.

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.

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.

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.

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.

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.

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.

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.

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field （RMF） theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov （HFB-14） model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.