Mean-field Calculations Research Articles

Triaxial deformation, shell structure, shell corrections and the connection to alpha-clustering in nuclei

Abstract We explore the connection between the appearance of quasi-stable structures in mean-field type calculations, which arise as a result of the evolution of the underlying shell structure as a function of deformation, and $\alpha$-clustering in light even-even nuclei. The Nilsson-Strutinsky mean-field approach employs a macroscopic liquid-drop whose energy is modified by a shell correction term derived using the Strutinsky method. This method reflects the variations in the energies of the single-particle states with deformation. As such, there is no obvious connection to clustering. 

Here we use the changing level scheme of the deformed harmonic oscillator as a function of triaxial deformation to fully explore the variation in stability of $\alpha$-cluster structures in light even-even nuclei. The energies of the harmonic oscillator levels are used to deduce the energy required to disrupt the $\alpha$-cluster as a function of the triaxial deformation. We find that there is good agreement between variations in the shell correction energy in the mean-field method and the energy required to disrupt the $\alpha$-cluster. This provides a necessary link between understanding of the appearance of quasi-stable $\alpha$-cluster structures and quasi-stable shapes appearing in mean-field calculations.

Use of Multigrids to Reduce the Cost of Performing Interpolative Separable Density Fitting.

In this article, we present an interpolative separable density fitting (ISDF)-based algorithm to calculate the exact exchange in periodic mean field calculations. In the past, decomposing the two-electron integrals into the tensor hypercontraction (THC) form using ISDF was the most expensive step of the entire mean field calculation. Here, we show that by using a multigrid-ISDF algorithm, both the memory and the CPU cost of this step can be reduced. The CPU cost is brought down from cubic scaling to quadratic scaling with a low computational prefactor which reduces the cost by almost 2 orders of magnitude. Thus, in the new algorithm, the cost of performing ISDF is largely negligible compared to other steps. Along with the CPU cost, the memory cost of storing the factorized two-electron integrals is also reduced by a factor of up to 35. With the current algorithm, we can perform Hartree-Fock calculations on a diamond supercell containing more than 17,000 basis functions and more than 1500 electrons on a single node with no disk usage. For this calculation, the cost of constructing the exchange matrix is only a factor of 4 slower than the cost of diagonalizing the Fock matrix. Augmenting our approach with linear scaling algorithms can further speed up the calculations.

Weyl nodes in Ce3Bi4Pd3 revealed by dynamical mean-field theory

Experimental studies have found unusual transport properties in Ce3Bi4Pd3 which are potentially a consequence of the interplay between band-structure topology and electronic correlations. Based on these measurements, the existence of Weyl points in strongly renormalized, flat quasiparticle bands has been postulated. However, so far there has been neither a direct spectroscopic observation of these nor a calculation from first principles that would confirm their existence close to the Fermi energy. Here we present density functional theory and dynamical mean-field theory calculations and study the low-energy excitations and their topological properties. We find that the Kondo effect promotes two out of the six angular momentum J=5/2 states, with the other four pushed to higher energies. Further, we find Weyl nodes close to the Fermi energy as previously suggested for explaining the observed giant spontaneous Hall effect in Ce3Bi4Pd3 as well as nodal lines. Published by the American Physical Society 2024

Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an Mth-order diagram at inverse temperature β and spectral width ωmax from O((βωmax)2M−1) for a direct quadrature to O(M(log(βωmax))M+1), with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca2RuO4, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. Published by the American Physical Society 2024

General Condition for Polymer Cononsolvency in Binary Mixed Solvents.

Starting from a generic model based on the thermodynamics of mixing and abstracted from the chemistry and microscopic details of solution components, three consistent and complementary computational approaches are deployed to investigate the general condition for polymer cononsolvency in binary mixed solvents at the zeroth order. The study reveals χPS - χPC + χSC as the underlying universal parameter that regulates cononsolvency, where χαβ is the immiscibility parameter between the α- and β-component. Two disparate cononsolvency regimes are identified for χPS - χPC + χSC < 0 and χPS - χPC + χSC > 2, respectively, based on the behavior of the second osmotic virial coefficient at varying solvent mixture composition x C. The predicted condition is verified using self-consistent field calculations by directly examining the polymer conformational transition as a function of x C. It is further shown that in the regime χPS - χPC + χSC < 0, the reentrant polymer conformation transition is driven by maximizing the solvent-cosolvent contact, but in the regime χPS - χPC + χSC > 2, it is driven by promoting polymer and cosolvent contact. In-between the two regimes when neither effect is dominant, a monotonic response of polymer conformation to x C is observed. Effects of the mean-field approximation on the predicted condition are evaluated by comparing the mean-field calculations with computer simulations. It shows that the fluctuation effects lead to a higher threshold value of χPS - χPC + χSC in the second regime, where local enrichment of cosolvent in polymer proximity plays a critical role.

A topological Hund nodal line antiferromagnet

The interplay of topology, magnetism, and correlations gives rise to intriguing phases of matter. In this study, through state-of-the-art angle-resolved photoemission spectroscopy, density functional theory, and dynamical mean-field theory calculations, we visualize a fourfold degenerate Dirac nodal line at the boundary of the bulk Brillouin zone in the antiferromagnet YMn2Ge2. We further demonstrate that this gapless, antiferromagnetic Dirac nodal line is enforced by the combination of magnetism, space-time inversion symmetry, and nonsymmorphic lattice symmetry. The corresponding drumhead surface states traverse the whole surface Brillouin zone. YMn2Ge2 thus serves as a platform to exhibit the interplay of multiple degenerate nodal physics and antiferromagnetism. Interestingly, the magnetic nodal line displays a d-orbital dependent renormalization along its trajectory in momentum space, thereby manifesting Hund’s coupling. Our findings offer insights into the effect of electronic correlations on magnetic Dirac nodal lines, leading to an antiferromagnetic Hund nodal line.

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground state shapes is shown with the neutron number, i.e., spherical shapes at shell closures N=126, 184, 258, and prolate dominated shapes between them. In analogy to the shape evolution, the inner fission barriers also exhibit a periodic behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect to the inner fission barrier is evaluated using the triaxial relativistic mean field calculations plus a simple BCS method for pairing. With the triaxial correction included, good consistency in the inner barrier heights is found with the available empirical data.&amp;#xD;Besides, the evolution from the proton to the neutron drip line is in accord with the results by the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus 318U which may play a role of fission recycling in the astrophysical r-process nucleosynthesis.&amp;#xD;

Observation of stacking engineered magnetic phase transitions within moiré supercells of twisted van der Waals magnets

Recent demonstrations of moiré magnetism, featuring exotic phases with noncollinear spin order in the twisted van der Waals (vdW) magnet chromium triiodide CrI3, have highlighted the potential of twist engineering of magnetic (vdW) materials. However, the local magnetic interactions, spin dynamics, and magnetic phase transitions within and across individual moiré supercells remain elusive. Taking advantage of a scanning single-spin magnetometry platform, here we report observation of two distinct magnetic phase transitions with separate critical temperatures within a moiré supercell of small-angle twisted double trilayer CrI3. By measuring temperature-dependent spin fluctuations at the coexisting ferromagnetic and antiferromagnetic regions in twisted CrI3, we explicitly show that the Curie temperature of the ferromagnetic state is higher than the Néel temperature of the antiferromagnetic one by ~10 K. Our mean-field calculations attribute such a spatial and thermodynamic phase separation to the stacking order modulated interlayer exchange coupling at the twisted interface of moiré superlattices.

Many-sided Poisson–Voronoi cells with only Gabriel neighbors

Let pnG be the probability for a planar Poisson–Voronoi cell to be n-sided and have only Gabriel neighbors. Using an exact coordinate transformation followed by scaling arguments and a mean-field type calculation, we obtain the asymptotic expansion of log⁡pnG in the limit of large n. We determine several statistical properties of a many-sided cell obeying this ‘Gabriel condition.’ In particular, the cell perimeter, when parametrized as a function τ(θ) of the polar angle θ, behaves as a Brownian bridge on the interval 0⩽θ⩽2π . We point out similarities and differences with related problems in random geometry.

Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory.

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.

Emergence of flat bands and ferromagnetic fluctuations via orbital-selective electron correlations in Mn-based kagome metal

Kagome lattice has been actively studied for the possible realization of frustration-induced two-dimensional flat bands and a number of correlation-induced phases. Currently, the search for kagome systems with a nearly dispersionless flat band close to the Fermi level is ongoing. Here, by combining theoretical and experimental tools, we present Sc3Mn3Al7Si5 as a novel realization of correlation-induced almost-flat bands in the kagome lattice in the vicinity of the Fermi level. Our magnetic susceptibility, 27Al nuclear magnetic resonance, transport, and optical conductivity measurements provide signatures of a correlated metallic phase with tantalizing ferromagnetic instability. Our dynamical mean-field calculations suggest that such ferromagnetic instability observed originates from the formation of nearly flat dispersions close to the Fermi level, where electron correlations induce strong orbital-selective renormalization and manifestation of the kagome-frustrated bands. In addition, a significant negative magnetoresistance signal is observed, which can be attributed to the suppression of flat-band-induced ferromagnetic fluctuation, which further supports the formation of flat bands in this compound. These findings broaden a new prospect to harness correlated topological phases via multiorbital correlations in 3d-based kagome systems.

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S=1/2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J, is considered, and the overall model becomes an effective XXZ model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024

One-Dimensional Magnetic Conduction Channels across Zigzag Graphene Nanoribbon/Hexagonal Boron Nitride Heterojunctions.

We examine the electronic structure of recently fabricated in-plane heterojunctions of zigzag graphene nanoribbons embedded in hexagonal boron nitride. We focus on hitherto unexplored interface configurations in which both edges of the nanoribbon are bonded to the same chemical species, either boron or nitrogen atoms. Using ab initio and mean-field Hubbard model calculations, we reveal the emergence of one-dimensional magnetic conducting channels at these interfaces. These channels originate from the energy shift of the magnetic interface states that is induced by charge transfer between the nanoribbon and hexagonal boron nitride. We further address the response of these heterojunctions to external electric and magnetic fields, demonstrating the tunability of energy and spin splittings in the electronic structure. Our findings establish that zigzag graphene nanoribbon/hexagonal boron nitride heterojunctions are a suitable platform for exploring and engineering spin transport in the atomically thin limit, with potential applications in integrated spintronic devices.

Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the π-meson and ρ-tensor (ρ-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l˜). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l˜ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the ρ-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.

Spontaneous breaking of the SO(2N) symmetry in the Gross-Neveu model

The canonical Gross-Neveu model for N two-component Dirac fermions in 2+1 dimensions suffers a continuous phase transition at a critical interaction gc1∼1/N at large N, at which its continuous symmetry SO(2N) is preserved and a discrete (Ising) symmetry becomes spontaneously broken. A recent mean-field calculation, however, points to an additional transition at a different critical gc2∼−Ngc1, at which SO(2N)→SO(N)×SO(N). To study the latter phase transition we rewrite the Gross-Neveu interaction g(ψ¯ψ)2 in terms of three different quartic terms for the single (L=1) 4N-component real (Majorana) fermion, and then extend the theory to L&gt;1. This allows us to track the evolution of the fixed points of the renormalization group transformation starting from L≫1, where one can discern three distinct critical points which correspond to continuous phase transitions into (1) SO(2N)-singlet mass-order-parameter, (2) SO(2N)-symmetric-tensor mass-order-parameters, and (3) SO(2N)-adjoint nematic-order-parameters, down to L=1 value that is relevant to the standard Gross-Neveu model. Below the critical value of Lc(N)≈0.35N for N≫1 only the Gross-Neveu critical point (1) still implies a diverging susceptibility for its corresponding (SO(2N)-singlet) order parameter, whereas the two new critical points that existed at large L ultimately become equivalent to the Gaussian fixed point at L=1. We interpret this metamorphosis of the SO(2N)-symmetric-tensor fixed point from critical to spurious as an indication that the transition at gc2 in the original Gross-Neveu model is turned first-order by fluctuations. Published by the American Physical Society 2024

Probing configuration of α clusters with spectator particles in relativistic heavy-ion collisions

We propose to use spectator particle yield ratios to probe the configuration of α clusters in 12C and 16O by their ultracentral collisions at RHIC and LHC energies. The idea is illustrated based on initial density distributions with various α-cluster configurations generated by a microscopic cluster model, and without α clusters from mean-field calculations. The multifragmentation of the spectator matter produces more spectator light nuclei including α clusters in collisions of nuclei with chain structure of α clusters, compared to those of nuclei with a more compact structure. The yield ratio of free spectator neutrons to spectator particles with mass-to-charge ratio A/Z=2 scaled by their masses can be practically measured by the zero-degree calorimeter (ZDC) at RHIC and LHC, serving as a clean probe free from modeling the complicated dynamics at midrapidities.

Verification of scaling behavior near dynamic phase transitions for nonantisymmetric field sequences.

We investigate the scaling behavior of the magnetic dynamic order parameter Q in the vicinity of the dynamic phase transition (DPT) in the presence of temporal field sequences H(t) that are periodic with period P but lack half-wave antisymmetry. We verify by means of mean-field calculations that the scaling of Q is preserved in the vicinity of the second-order phase transition if one defines a suitable generalized conjugate field H^{*} that reestablishes the proper time-reversal symmetry. For the purpose of our quantitative data analysis, we employ the dynamic equivalent of the Arrott-Noakes equation of state, which allows for a simultaneous scaling analysis of the period P and the conjugate-field H^{*} dependence of Q. By doing so, we demonstrate that both the scaling behavior and universality are preserved, even if the dynamics is driven by a more general applied field sequence that lacks antisymmetry.

Suppression of polaron self-localization by correlations

We investigate self-localization of a polaron in a homogeneous Bose-Einstein condensate in one dimension. This effect, where an impurity is trapped by the deformation that it causes in the surrounding Bose gas, has been first predicted by mean-field calculations, but has not been seen in experiments. We study the system in one dimension, where, according to the mean-field approximation, the self-localization effect is particularly robust and present for arbitrarily weak impurity-boson interactions. We address the question whether self-localization is a real effect by developing a variational method which incorporates impurity-boson correlations nonperturbatively and solving the resulting inhomogeneous correlated polaron equations. We find that correlations inhibit self-localization except for very strongly repulsive or attractive impurity-boson interactions. Our prediction for the critical interaction strength for self-localization agrees with a sharp drop of the inverse effective mass found in quantum Monte Carlo simulations of polarons in one dimension. Published by the American Physical Society 2024

Hartree–Fock Mean Field Calculations with Random Phase Approximation for 140Ce Nuclei Structure

Hartree–Fock Mean Field Calculations with Random Phase Approximation for 140Ce Nuclei Structure

Origins of multi-sublattice magnetism and superexchange interactions in double–double perovskite CaMnCrSbO6

The multi-sublattice magnetism and electronic structure in double–double perovskite compound CaMnCrSbO6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order ( TC∼ 49 K) between between Mn2+ and Cr3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d-orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases with Ueff (U − J), thereby showing a Mott–Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)–O–Mn(2) (out of plane and in-plane), Mn(1)–O–Cr and Mn(2)–O–Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr–O–O–Cr super-superexchange is found to be ferromagnetic. The Mn(2)–O–Cr superexchange is weaker than the Mn(1)–O–Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strength JAFM and also for the weaker ferromagnetic JFM . The relative strengths of JAFM for the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr–O–O–Cr super-superexchange strength ( J~SS ), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn2+ spins and a single magnetic sublattice for Cr3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C .