Mean-field Calculations Research Articles

Shape phase transitions in odd−A Zr isotopes

Spectroscopic properties that characterize shape phase transitions in neutron-rich odd-A Zr isotopes are investigated using the framework of nuclear density functional theory and particle-core coupling. The interacting-boson Hamiltonian of the even-even core nuclei, and the single-particle energies and occupation probabilities of the unpaired neutron are completely determined by deformation constrained self-consistent mean-field calculations based on the relativistic Hartree-Bogoliubov model with a choice of a universal energy density functional and pairing interaction. The triaxial $(\beta,\gamma)$ deformation energy surfaces for even-even $^{94-102}$Zr indicates transition from triaxial or $\gamma$-soft ($^{94,96}$Zr) to prolate ($^{98}$Zr), and triaxial ($^{100,102}$Zr) shapes. The corresponding low-energy excitation spectra of the odd-A Zr isotopes are in very good agreement with recent experimental results. Consistent with the structural evolution of the neighboring even-even Zr nuclei, the state-dependent effective deformations and their fluctuations in the odd-A isotopes indicate a pronounced discontinuity around the transitional nucleus $^{99}$Zr.

Pressure-induced incommensurate antiferromagnetic order in a ferromagnetic B -site ordered double-perovskite Lu2NiMnO6

We have investigated the pressure effect on magnetic ordering of the ferromagnetic double perovskite ${\mathrm{Lu}}_{2}{\mathrm{NiMnO}}_{6}$ by magnetization, ac magnetic susceptibility, and neutron diffraction experiments up to 8.0 GPa in order to understand the ferromagnetic-to-antiferromagnetic phase transition by substitution of the $A$ sites in ${A}_{2}{\mathrm{NiMnO}}_{6}$ from rare-earth to indium or scandium ions. Strong ferromagnetic spin correlation seen in the susceptibility at low pressure is significantly suppressed by increasing pressure. In a neutron diffraction experiment, the magnetic Bragg reflections associated with ferromagnetic ordering disappear above 4.5 GPa. For the high-pressure region above 4.5 GPa, an antiferromagnetic ordering with long-period incommensurate modulation appears, which is coexistent with ferromagnetic short-range order. From mean-field calculations, we infer that pressure modification of the delicate balance of the competing next-nearest-neighbor exchange interactions between Ni and Ni, or Mn and Mn, plays an important role in the phase transition from ferromagnetic to antiferromagnetic ordering in ${A}_{2}{\mathrm{NiMnO}}_{6}$.

Exotic nuclear shape due to cluster formation at high angular momentum

It is shown, for the first time, how the exotic shapes due to cluster formation at high excitation energy and angular momentum are manifested through giant dipole resonance (GDR) strength function under the framework of the extended quantum molecular dynamics (EQMD) model. The results of EQMD calculation are compared with the existing experimental data of $^{32}\mathrm{S}$ and $^{28}\mathrm{Si}$ formed in the reactions $^{20}\mathrm{Ne}+^{12}\mathrm{C}$ and $^{16}\mathrm{O}+^{12}\mathrm{C}$, respectively, at high angular momenta. It is found that the EQMD predicts the general trend of the experimental GDR strength functions for $^{32}\mathrm{S}$ and $^{28}\mathrm{Si}$ by considering the ring or toroidal configuration, whereas the linear chain configurations with $\ensuremath{\alpha}$ clusters can reproduce the higher-energy peak in $^{32}\mathrm{S}$ and $^{28}\mathrm{Si}$. Thus, the direct signature of the cluster formation at high temperature and angular momentum is the observation of a GDR peak $\ensuremath{\approx}25\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ which cannot be predicted within the mean-field calculations. The present result highlights the role of $\ensuremath{\alpha}$ cluster states above the decay threshold, which is still an open field of investigation.

Orbital selective spin waves in detwinned NaFeAs

The existence of orbital-dependent electronic correlations has been recognized as an essential ingredient to describe the physics of iron-based superconductors. NaFeAs, a parent compound of iron based superconductors, exhibits a tetragonal-to-orthorhombic lattice distortion below $T_s\approx 60$ K, forming an electronic nematic phase with two 90$^\circ$ rotated (twinned) domains, and orders antiferromagnetically below $T_N\approx 42$ K. We use inelastic neutron scattering to study spin waves in uniaxial pressure-detwinned NaFeAs. By comparing the data with combined density functional theory and dynamical mean-field theory calculations, we conclude that spin waves up to an energy scale of $E_\text{crossover} \approx 100$ meV are dominated by $d_{yz}$-$d_{yz}$ intra-orbital scattering processes, which have the two-fold ($C_2$) rotational symmetry of the underlying lattice. On the other hand, the spin wave excitations above $E_\text{crossover}$, which have approximately fourfold ($C_4$) rotational symmetry, arise from the $d_{xy}$-$d_{xy}$ intra-orbital scattering that controls the overall magnetic bandwidth in this material. In addition, we find that the low-energy ($E\approx 6$ meV) spin excitations change from approximate $C_4$ to $C_2$ rotational symmetry below a temperature $T^\ast$ ($>T_s$), while spin excitations at energies above $E_\text{crossover}$ have approximate $C_4$ rotational symmetry and are weakly temperature dependent. These results are consistent with angle resolved photoemission spectroscopy measurements, where the presence of an uniaxial strain necessary to detwin NaFeAs also raises the onset temperature $T^\ast$ of observable orbital-dependent band splitting to above $T_s$, thus supporting the notion of orbital selective spin waves in the nematic phase of iron-based superconductors.

Statistical error estimates in dynamical mean-field theory and extensions thereof

We employ the jackknife algorithm to analyze the propagation of the statistical quantum Monte Carlo error through the Bethe--Salpeter equation. This allows us to estimate the error of dynamical mean-field theory calculations of the susceptibility and of dynamical vertex approximation calculations of the self-energy. We find that the different frequency components of the susceptibility are uncorrelated, whereas those of the self-energy are correlated. For improving the quality of the correlation matrix taking sufficiently many jackknife bins is key, while for reducing the standard error of the mean sufficiently many Monte Carlo measurements are necessary. We furthermore show that even in the case of the self-energy, the finite covariance does not have a sizable influence on the analytic continuation.

Magnetic properties of (Fe1-xMnx)2AlB2 and the impact of substitution on the magnetocaloric effect.

In this work, we investigate the magnetic structures of (Fe1-xMnx)2AlB2 solid-solution quaternaries in the to 1 range using x-ray and neutron diffraction, magnetization measurements, and mean-field theory calculations. While Fe2AlB2 and Mn2AlB2 are known to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively, herein we focused on the magnetic structure of their solid solutions, which is not well understood. The FM ground state of Fe2AlB2 becomes a canted AFM at , with a monotonically diminishing FM component until . The FM transition temperature () decreases linearly with increasing . These changes in magnetic moments and structures are reflected in anomalous expansions of the lattice parameters, indicating a magnetoelastic coupling. Lastly, the magnetocaloric properties of the solid solutions were explored. For the isothermal entropy change is smaller by 30% than it is for Fe2AlB2, while the relative cooling power is larger by 6%, due to broadening of the temperature range of the transition.

Atomically Precise Synthesis and Characterization of Heptauthrene with Triplet Ground State.

By virtue of multitunable spin structures upon designing the π-electron topologies, phenalenyl-based nanographenes are of substantial interest in fundamental science and for potential applications in spintronics. Heptauthrene, as one of the well-known phenalenyl diradicals, is composed of one benzene-fused bisphenalenyls in mirror symmetry and expected to have a triplet ground state. However, the synthesis of unsubstituted heptauthrene remains very challenging due to the high reactivity of triplet diradicals. Here, we report a combined in-solution and on-surface synthesis of unsubstituted heptauthrene, whose chemical structure is characterized through bond-resolved atomic force microscopy. Combined with mean-field Hubbard model calculations, its triplet ground state is unambiguously confirmed by the underscreened Kondo resonance in response to the magnetic field, as well as the engineered spin-state switching upon extra hydrogen atom addition and dissociation on the radical site. Our results provide access to phenalenyl-based nanographenes with high-spin ground state, potentially useful in constructing high-spin networks.

Functional renormalization group study of the critical region of the quark-meson model with vector interactions

The critical region of the two flavour quark-meson model with vector interactions is explored using the Functional Renormalization Group, a non-perturbative method that takes into account quantum and thermal fluctuations. Special attention is given to the low temperature and high density region of the phase diagram, which is very important to construct the equation of state of compact stars. As in previous studies, without repulsive vector interaction, an unphysical region of negative entropy density is found near the first order chiral phase transition. We explore the connection between this unphysical region and the chiral critical region, especially the first order line and spinodal lines, using also different values for vector interactions. We find that the unphysical negative entropy density region appears because the s=0 isentropic line, near the critical region, is displaced from its T=0 location. For certain values of vector interactions this region is pushed to lower temperatures and high chemical potentials in such way that the negative entropy density region on the phase diagram can even disappear. In the case of finite vector interactions, the location of the critical end point has a non-trivial behaviour in the T-mu _B plane, which differs from that in mean field calculations.

Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields.

We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a nontrivial reconstruction of symmetry generators from the standard spin and quadrupolar description. We also perform a semiclassical MonteCarlo simulation to show that thermal fluctuations prefer the same three phases as well. Moreover, we find that exotic topological phase transitions driven by the binding-unbinding of fractional (half-)vortices take place, due to the nematicity of the low- and high-field phases. Possible experimental realization with alkaline-earth-like cold atoms is also discussed.

First-Principles Quantum and Quantum-Classical Simulations of Exciton Diffusion in Semiconducting Polymer Chains at Finite Temperature.

We report on first-principles quantum-dynamical and quantum-classical simulations of photoinduced exciton dynamics in oligothiophene chain segments, representative of intrachain exciton migration in the poly(3-hexylthiophene) (P3HT) polymer. Following up on our recent study (Binder R.; Burghardt, I. Faraday Discuss. 2020, 221, 406), multilayer multiconfiguration time-dependent Hartree calculations for a short oligothiophene segment comprising 20 monomer units (OT-20) are carried out to obtain full quantum-dynamical simulations at finite temperature. These are employed to benchmark mean-field Ehrenfest calculations, which are shown to give qualitatively correct results for the present system. Periodic boundary conditions turn out to significantly improve earlier estimates of diffusion coefficients. Using the Ehrenfest approach, a series of calculations are subsequently carried out for larger lattices (OT-40 to OT-80), leading to estimates for temperature-dependent mean-squared displacements, which are found to exhibit a near-linear dependence as a function of time. The resulting diffusion coefficient estimates are an increasing function of temperature, whose detailed functional form depends on the degree of static disorder. With a realistic static disorder parameter (σs ≃ 0.06 eV), the diffusion coefficients decrease from D ∼ 1 × 10-2 cm2 s-1 to D ∼ 1 × 10-3 cm2 s-1, in qualitative agreement with experimental data for P3HT. The dynamical scenario obtained from our simulations shows that exciton migration in P3HT-type chains is a largely adiabatic process throughout the temperature regime we investigated (i.e., T = 50-300 K). The resulting picture of exciton migration is a coherent, but not bandlike, motion of an exciton-polaron driven by fluctuations induced by low-frequency modes. This process acquires partial hopping character if static disorder becomes prominent and Anderson localization sets in.

Configurational thermodynamics of a 1/2〈111〉 screw dislocation core in Mo–W solid solutions using cluster expansion

In this work, we have developed a methodology to obtain an ab initio cluster expansion of a system containing a dislocation and studied the effect of configurational disorder on the 1/2〈111〉 screw dislocation core structure in disordered Mo1−xWx alloys. Dislocation cores control the selection of glide planes, cross slip, and dislocation nucleation. Configurational disorders in alloys can impact the dislocation core structure and affect dislocation mobility. For our calculations, we have used a quadrupolar periodic array of screw dislocation dipoles and obtained the relaxed structures and energies using density functional theory. We have obtained the dislocation core structure as a function of composition and the interaction energies of solutes with the dislocation as a function of position with respect to the core. With these energies, we performed mean-field calculations to assess segregation toward the core. Finally, with the calculated energies of 1848 alloy configurations with different compositions, we performed a first principle cluster expansion of the configurational energetics of Mo1−xWx solid solutions containing dislocations.

Rare-Earths (Pr, Pm, Sm, Dy, and Tm)-Doped SnO2: Ab Initio, Mean Field, and Monte Carlo Calculation

In this paper, we consider the electronic and magnetic proprieties of five rare-earths (RE = Pr, Pm, Sm, Dy, and Tm)-doped Tin (IV) oxide semiconductor Sn1 − xRExO2 (x = 0.10) in the rutile structure. The presence of the 4f orbitals in our structures pushes us to choose the local density approximation with Self-interaction-corrected (LDA-SIC) to improve the obtained results. We also discuss the critical temperature retrieved from the study the total magnetizations and the susceptibilities using Monte Carlo simulations for each rare-earth element used.

NESSi: The Non-Equilibrium Systems Simulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time N points and a high-order implementation of integration routines. The total integrated error scales up to O(N−7), which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers. Program summaryProgram Title: NESSiCPC Library link to program files:http://dx.doi.org/10.17632/973crf9hgd.1Licensing provisions: MPL v2.0Programming language: C++, pythonExternal routines/libraries: cmake, eigen3, hdf5 (optional), mpi (optional), omp (optional)Nature of problem: Solves equations of motion of time-dependent Green’s functions on the Kadanoff–Baym contour.Solution method: Higher-order solution methods of integral and integro-differential equations on the Kadanoff–Baym contour.

Application of a helicity proxy to edge-on galaxies

ABSTRACT We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity.

Exact solution of multiangle quantum many-body collective neutrino-flavor oscillations

I study the flavor evolution of a dense neutrino gas by considering vacuum contributions, matter effects and neutrino self-interactions. Assuming a system of two flavors in a uniform matter background, the time evolution of the many-body system in discretized momentum space is computed. The multi-angle neutrino-neutrino interactions are treated exactly and compared to both the single-angle approximation and mean field calculations. %The time unit chosen is $\mu_0^{-1}=(\frac{G_F}{2\sqrt{2}V})^{-1}$. The mono-energetic two neutrino beam scenario is solved analytically. I proceed to solve flavor oscillations for mono-energetic cubic lattices and quadratic lattices of two energy levels. In addition I study various configurations of twelve, sixteen, and twenty neutrinos. I find that when all neutrinos are initially of the same flavor, all methods agree. When both flavors are present, I find collective oscillations and flavor equilibration develop in the many body treatment but not in the mean field method. This difference persists in dense matter with tiny mixing angle and it can be ascribed to non-negligible flavor polarization correlations being present. Entanglement entropy is significant in all such cases. The relevance for supernovae or neutron stars mergers is contingent upon the value of the normalization volume $V$ and the large $N$ dependence of the timescale associated with oscillations. In future work, I intend to study this dependence using larger lattices and also include anti-neutrinos.

Intrinsic Ion Transport Properties of Block Copolymer Electrolytes.

Knowledge of intrinsic properties is of central importance for materials design and assessing suitability for specific applications. Self-assembling block copolymer electrolytes (BCEs) are of great interest for applications in solid-state energy storage devices. A fundamental understanding of ion transport properties, however, is hindered by the difficulty in deconvoluting extrinsic factors, such as defects, from intrinsic factors, such as the presence of interfaces between the domains. Here, we quantify the intrinsic ion transport properties of a model BCE system consisting of poly(styrene-block-ethylene oxide) (SEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt using a generalizable strategy of depositing thin films on interdigitated electrodes and self-assembling fully connected parallel lamellar structures throughout the films. Comparison between conductivity in homopolymer poly(ethylene oxide) (PEO)-LiTFSI electrolytes and the analogous conducting material in SEO over a range of salt concentrations (r, molar ratio of lithium ion to ethylene oxide repeat units) and temperatures reveals that between 20% and 50% of the PEO in SEO is inactive. Using mean-field theory calculations of the domain structure and monomer concentration profiles at domain interfaces-both of which vary substantially with salt concentration-the fraction of inactive PEO in the SEO, as derived from conductivity measurements, can be quantitatively reconciled with the fraction of PEO that is mixed with greater than a few volume percent of polystyrene. Despite the detrimental interfacial effects for ion transport in BCEs, the intrinsic conductivity of the SEO studied here (ca. 10-3 S/cm at 90 °C, r = 0.085) is an order of magnitude higher than reported values from bulk samples of similar molecular weight SEO (ca. 10-4 S/cm at 90 °C, r = 0.085). Overall, this work provides motivation and methods for pursuing improved BCE chemical design, interfacial engineering, and processing.

Time-dependent generator coordinate method study of fission: Mass parameters

Collective mass tensors derived in the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method are employed in a study of induced fission dynamics. Together with a collective potential determined in deformation-constrained self-consistent mean-field calculations based on nuclear energy density functionals, the mass tensors specify the collective Hamiltonian that governs the time evolution of the nuclear wave function from an initial state at equilibrium deformation, up to scission and the formation of fission fragments. In an illustrative calculation of low-energy induced fission of $^{228}$Th, $^{230}$Th, $^{234}$U, and $^{240}$Pu, we compare the non-perturbative and perturbative cranking ATDHFB mass tensors in the plane of axially-symmetric quadrupole and octupole deformations, as well as the resulting charge yields.

Strength of pairing interaction for hyperons in multistrangeness hypernuclei

Pairing correlations play a very important role in atomic nuclei. Although several effective pairing interactions have been used in mean field calculations for nucleons, little is known about effective pairing interactions for hyperons. Based on the quark model, we propose a relationship between effective pairing interactions for hyperons and for nucleons; e.g., for Λs, the strength of the pairing interaction is 4/9 of that for nucleons. A separable pairing force of finite range which has been widely applied to describing pairing correlations in normal nuclei is used to investigate pairing effects in multi-Λ Ca, Sn and Pb hypernuclei.

Shape coexistence revealed in the $$N=Z$$ isotope $$^{72}$$Kr through inelastic scattering

The $N=Z=36$ nucleus $^{72}$Kr has been studied by inelastic scattering at intermediate energies. Two targets, $^{9}$Be and $^{197}$Au, were used to extract the nuclear deformation length, $\delta_\text{N}$, and the reduced $E2$ transition probability, $B(E2)$. The previously unknown non-yrast $2^+$ and $4^+$ states as well as a new candidate for the octupole $3^-$ state have been observed in the scattering on the Be target and placed in the level scheme based on $\gamma-\gamma$ coincidences. The second $2^+$ state was also observed in the scattering on the Au target and the $B(E2;\;2^+_2 \rightarrow 0^+_1)$ value could be determined for the first time. Analyzing the results in terms of a two-band mixing model shows clear evidence for a oblate-prolate shape coexistence and can be explained by a shape change from an oblate ground state to prolate deformed yrast band from the first $2^+$ state. This interpretation is corroborated by beyond mean field calculations using the Gogny D1S interaction.

Skyrme-type nuclear interaction as a tool for calculating the finite-nuclear-size correction to atomic energy levels and the bound-electron g factor

A state-of-the-art approach for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor is introduced and demonstrated for a series of highly charged hydrogen-like ions. Firstly, self-consistent mean-field calculations based on the Skyrme-type nuclear interaction are employed in order to produce a realistic nuclear proton distribution. In the second step, the obtained nuclear charge density is used to construct the potential of an extended nucleus, and the Dirac equation is solved numerically. The ambiguity in the choice of a Skyrme parametrization is supressed by fine-tuning of only one parameter of the Skyrme force in order to accurately reproduce the experimental values of nuclear radii in each particular case. The homogeneously charged sphere approximation, the two-parameter Fermi distribution and experimental nuclear charge distributions are used for comparison with our approach, and the uncertainties of the presented calculations are estimated. In addition, suppression of the finite nuclear size effect for the specific differences of $g$ factors is demonstrated.