Short-range Dynamical Correlations Research Articles

Electronic correlation in nearly free electron metals with beyond-DFT methods

For more than three decades, nearly free-electron elemental metals have been a topic of debate because the computed bandwidths are significantly wider in the local density approximation to density-functional theory (DFT) than indicated by angle-resolved photoemission (ARPES) experiments. Here, we systematically investigate this using first principles calculations for alkali and alkaline-earth metals using DFT and various beyond-DFT methods such as meta-GGA, G0W0, hybrid functionals (YS-PBE0, B3LYP), and LDA + eDMFT. We find that the static non-local exchange, as partly included in the hybrid functionals, significantly increase the bandwidths even compared to LDA, while the G0W0 bands are only slightly narrower than in LDA. The agreement with the ARPES is best when the local approximation to the self-energy is used in the LDA + eDMFT method. We infer that even moderately correlated systems with partially occupied s orbitals, which were assumed to approximate the uniform electron gas, are very well described in terms of short-range dynamical correlations that are only local to an atom.

Doping phase diagram of a Hubbard model for twisted bilayer cuprates

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $\theta=53.13^{\circ}$ using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference $\phi$ between the $d$-wave order parameters of two layers is $\pi$ in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference $\phi$ changes continuously from 0 to $\pi$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.

Molecular multibond dissociation with small complete active space augmented by correlation density functionals.

Molecular multibond dissociation displays a variety of electron correlation effects posing a challenge for theoretical description. We propose a CASΠ(M)DFT approach, which includes these effects in an efficient way by combining the complete active space self-consistent field method with density functional theory (DFT). Within CASΠ(M)DFT, a small complete active space (CAS) accounts for the long-range intrabond and middle-range interbond nondynamic correlation in the stretched bonds. The common short-range dynamic correlation is calculated with the Lee-Yang-Parr (LYP) correlation DFT functional corrected for the suppression of dynamic correlation with nondynamic correlation. The remaining middle-range interbond dynamic correlation is evaluated with the modified LYP functional of the bond densities. As a result, CASΠ(M)DFT potential energy curves (PECs) calculated in the relatively small triple-zeta basis closely reproduce the benchmark complete basis set PECs for the following prototype multibonded molecules: N2, CO, H2O, and C2.

Semiclassical Dispersion Corrections Efficiently Improve Multiconfigurational Theory with Short-Range Density-Functional Dynamic Correlation.

Multiconfigurational wave functions are known to describe the electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamic correlation originating from the many configurations involving excitations out of the restricted orbital space, the active space, must be considered. Standard procedures involve approximations that eventually limit the ultimate accuracy achievable (most prominently, multireference perturbation theory). At the same time, the computational cost increases dramatically due to the necessity to obtain higher-order reduced density matrices. It is this disproportion that leads us here to propose an MC-srDFT-D hybrid approach of semiclassical dispersion (D) corrections to cover long-range dynamic correlation in a multiconfigurational (MC) wave function theory, which includes short-range (sr) dynamic correlation by density functional theory (DFT) without double counting. We demonstrate that the reliability of this approach is very good (at negligible cost), especially when considering that standard second-order multireference perturbation theory usually overestimates dispersion interactions.

Comparative study of proton and positive kaon interactions with carbon: hint of new physics like partial restoration of chiral symmetry in nuclei

Concerning the scattering of K+ - mesons on nuclei, the explicit discrepancy between experimental data and optical model calculations is a longstanding problem and none of the conventional medium effect corrections improves significantly the agreement with the data. In this paper the cross sections for the reactions K++12C at incident momenta of the kaon Plab < 800 MeV/c are calculated on the basis of Glauber’s high-energy approximation. The noneikonal corrections, Fermi motion effect and both Pauli and dynamic short-range correlations were incorporated in the Glauber approach for nuclear collisions. The influence of all these corrections on the calculation of the cross sections for the interactions of kaon with nucleus is discussed. The full calculations is compared to available data. The corrections seem to fail in reproducing the experimental data. Our results is compared to optical model calculations. We show that both our model and optical model fails to give a satisfactory description of K+-nuclei cross sections. Different attempts to remove this discrepancy with the in-medium effects taken into account are discussed.

Reproducing benchmark potential energy curves of molecular bond dissociation with small complete active space aided with density and density-matrix functional corrections.

Various effects of electron correlation accompany molecular bond dissociation, which makes the efficient calculation of potential energy curves a notoriously difficult problem. In an attempt to reliably reproduce both absolute energies and shapes of the benchmark dissociation curves, calculations with the combined CASΠDFT method are carried out for the prototype molecules H2, BH, F2, and N2. The complete active space (CAS) part of CASΠDFT accounts for long-range nondynamic correlation, while short-range dynamic correlation is accounted for with the corrected Lee-Yang-Parr correlation functional of density functional theory (DFT). The correction represents the suppression of dynamic correlation with nondynamic correlation, and it is a function of the ratio x(r) between the conditional and conventional densities obtained with the CAS on-top pair density Π(r). For the single-bonded molecules H2, BH, and F2, CASΠDFT succeeds in reproducing the shapes and absolute energies (for H2 and BH) of the benchmark curves, while for the triple-bonded N2 molecule, the addition to CASΠDFT of a multibond correction is required. It accounts for the middle-range dynamic correlation of the same-spin electrons in the (symmetrized) high-spin atomic electron configurations of the dissociating N2.

New Insights about CuO Nanoparticles from Inelastic Neutron Scattering.

Inelastic Neutron Scattering (INS) spectroscopy has provided a unique insight into the magnetodymanics of nanoscale copper (II) oxide (CuO). We present evidence for the propagation of magnons in the directions of the ordering vectors of both the commensurate and helically modulated incommensurate antiferromagnetic phases of CuO. The temperature dependency of the magnon spin-wave intensity (in the accessible energy-range of the experiment) conforms to the Bose population of states at low temperatures (T ≤ 100 K), as expected for bosons, then intensity significantly increases, with maximum at about 225 K (close to TN), and decreases at higher temperatures. The obtained results can be related to gradual softening of the dispersion curves of magnon spin-waves and decreasing the spin gap with temperature approaching TN on heating, and slow dissipation of the short-range dynamic spin correlations at higher temperatures. However, the intensity of the magnon signal was found to be particle size dependent, and increases with decreasing particle size. This “reverse size effect” is believed to be related to either creation of single-domain particles at the nanoscale, or “superferromagnetism effect” and the formation of collective particle states.

Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further discuss the role of the self-consistency condition and show that the approximation behaves as an asymptotic series at low temperature.

On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin.

Separate, one-parameter, on-top density functionals are derived for the short-range dynamic correlation between opposite and parallel-spin electrons, in which the electron-electron cusp is represented by an exponential function. The combination of both functionals is referred to as the Opposite-spin exponential-cusp and Fermi-hole correction (OF) functional. The two parameters of the OF functional are set by fitting the ionization energies and electron affinities, of the atoms He to Ar, predicted by ROHF in combination with the OF functional to the experimental values. For ionization energies, the overall performance of ROHF-OF is better than completely renormalized coupled-cluster [CR-CC(2,3)] and better than, or as good as, conventional density functional methods. For electron affinities, the overall performance of ROHF-OF is less impressive. However, for both ionization energies and electron affinities of third row atoms, the mean absolute error of ROHF-OF is only 3 kJ mol-1.

Strong coupling between localized 5f moments and itinerant quasiparticles in the ferromagnetic superconductor UGe2**Project supported by the National Natural Science Foundation of China (Grant No. 11404297), the Science Challenge Project (Grant No. TZ2016004), and the Science and Technology Foundation of China Academy of Engineering Physics (Grant Nos. 2013B0301050 and 2014A0301013).

The heavy fermion physics arises from the complex interplay of nearly localized 4f/5f electrons and itinerant band-like ones, yielding heavy quasiparticles with an effective mass about 100 times (or more) of the bare electrons. Recently, experimental and theoretical investigations point out a localized and delocalized dual nature in actinide compounds, where itinerant quasiparticles account for the unconventional superconductivity in the vicinity of a magnetic instability. Here we report the strong coupling between localized 5f moments and itinerant quasiparticles in the ferromagnetic superconductor UGe2. The coupling is nearly antiferromagnetic. As embedded in the ferromagnetic matrix of localized 5f moments below , this coupling leads to short-range dynamic correlations of heavy quasiparticles, characterized by fluctuations of magnetic clusters. Those cluster-like spins of itinerant quasiparticles show a broad hump of magnetization at , which is typical for the spin-glass freezing. Thus, our results present the direct observation of itinerant quasiparticles coexisting with localized 5f moments by conventional magnetic measurements, providing a new route into the coexistence between ferromagnetism and superconductivity in heavy fermion systems.

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron.

The hydrated electron, e-(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e-(aq) is still the subject of controversy. In particular, the structure of e-(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e-(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e-(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

Local Jahn-Teller distortions and orbital ordering inBa3Cu1+xSb2−xO9investigated by neutron scattering

A spin-orbital quantum liquid state is theoretically proposed in the honeycomb lattice of ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$, enabled by dynamic short-range correlations between the spin and orbital degrees of freedom. Using neutron diffraction, the local atomic structure of ${\mathrm{Ba}}_{3}{\mathrm{Cu}}_{1+x}{\mathrm{Sb}}_{2\ensuremath{-}x}{\mathrm{O}}_{9}$ at $x=0$ and 0.1 is obtained via the pair density function analysis. The results indicate that both compositions exhibit local Jahn-Teller (JT) distortions with the elongated ${\mathrm{CuO}}_{3}$ octahedral configuration. In ${\mathrm{Ba}}_{3}{\mathrm{Cu}}_{1.1}{\mathrm{Sb}}_{1.9}{\mathrm{O}}_{9}$, JT ordering of the distorted ${\mathrm{CuO}}_{3}$ octahedra gives rise to the orthorhombic symmetry with ferro-orbital order. On the other hand, in ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$, even though the ${\mathrm{CuO}}_{3}$ octahedra are JT distorted, there is no long-range ordering hence the symmetry is hexagonal. Furthermore, the local singlet excitation at 5.8 meV observed in ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ below 50 K is absent in ${\mathrm{Ba}}_{3}{\mathrm{Cu}}_{1.1}{\mathrm{Sb}}_{1.9}{\mathrm{O}}_{9}$. Instead, an excitation at 2.5 meV is observed in the latter, which is likely associated with short-range spin order.

Field-induced magnetic instability and quantum criticality in the antiferromagnet CeCu2Ge2.

The magnetic quantum criticality in strongly correlated electron systems has been considered to be closely related with the occurrence of unconventional superconductivity. Control parameters such as magnetic field, pressure or chemical doping are frequently used to externally tune the quantum phase transition for a deeper understanding. Here we report the research of a field-induced quantum phase transition using conventional bulk physical property measurements in the archetypal antiferromagnet CeCu2Ge2, which becomes superconductive under a pressure of about 10 GPa with Tc ~ 0.64 K. We offer strong evidence that short-range dynamic correlations start appearing above a magnetic field of about 5 T. Our demonstrations of the magnetic instability and the field-induced quantum phase transition are crucial for the quantum criticality, which may open a new route in experimental investigations of the quantum phase transition in heavy-fermion systems.

Momentum-space structure of quasielastic spin fluctuations inCe3Pd20Si6

Among heavy-fermion metals, Ce$_3$Pd$_{20}$Si$_6$ is one of the heaviest-electron systems known to date. Here we used high-resolution neutron spectroscopy to observe low-energy magnetic scattering from a single crystal of this compound in the paramagnetic state. We investigated its temperature dependence and distribution in momentum space, which was not accessible in earlier measurements on polycrystalline samples. At low temperatures, a quasielastic magnetic response with a half-width {\Gamma}=0.1 meV persists with varying intensity all over the Brillouin zone. It forms a broad hump centered at the (111) scattering vector, surrounded by minima of intensity at (002), (220) and equivalent wave vectors. The momentum-space structure distinguishes this signal from a simple crystal-field excitation at 0.31 meV, suggested previously, and rather lets us ascribe it to short-range dynamical correlations between the neighboring Ce ions, mediated by the itinerant heavy f-electrons via the RKKY mechanism. With increasing temperature, the energy width of the signal follows the conventional T$\scriptstyle^{1/2}$ law, {\Gamma}(T) = {\Gamma}$_0$ + A*T$\scriptstyle^{1/2}$. The momentum-space symmetry of the quasielastic response suggests that it stems from the simple-cubic Ce sublattice occupying the 8c Wyckoff site, whereas the crystallographically inequivalent 4a site remains magnetically silent in this material.

Compact two-electron wave function for bond dissociation and Van der Waals interactions: a natural amplitude assessment.

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.

Quasifree scattering of electrons on light nuclei and some properties of nuclear interaction

The status of experimental and theoretical studies of the position of the quasifree cross-section maximum in the A(e, e′) reaction is discussed. The dependence of the shift of the maximum relative to the elastic eN-scattering on the kinematic conditions of measurements is considered. The possibilities of using the data for the selection of realistic models of nucleon-nucleon interaction and dynamic short-range correlations in nuclei, as well as for determining the parameters of the nucleon-nucleus potential and the nucleon effective mass, are analyzed.

Self-consistent many-body perturbation theory in range-separated density-functional theory: A one-electron reduced-density-matrix-based formulation

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schr\"odinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this ``self-consistency problem'' and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order M\o{}ller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid G\"orling-Levy-type MBPT-DFT model.

Chapter 10 - Exact Theoretical Studies of Small Hubbard Clusters

Publisher Summary The ability to synthesize small clusters containing a few atoms provides an opportunity to examine and tune fundamental physical and chemical properties. Numerical methods can provide significant insight. This chapter describes a number of surprising and novel results obtained using a combination of exact diagonalization of a many-body Hamiltonian and statistical mechanics. Microscopic studies, which account accurately for short-range dynamical correlations in finite clusters, are relevant with regard to understanding the physics of the underdoped high T c superconductors (HTSCs). Such studies are also relevant to nanomagnetism and spintronics applications. The geometry of an elementary building block (cluster), its orientation, shape, and position in two and three dimensions can be controlled in a multidimensional parameter space of interaction strength, magnetic field, electron concentration, and temperature. In a recent study, it was concluded that inhomogeneous clustered states should be considered as a new paradigm in condensed matter physics. The method developed in this chapter can be used to describe magnetic instabilities in the spin-tetrahedral systems in terms of weakly coupled tetrahedrons with a singlet-triplet gap and low-lying singlets. The (thermodynamical) theory presented provides a mechanism of phase separation into carrier-rich and carrier-poor regions observed in the HTSC cuprates; it has been able to predict some of the observations related to local electron pairing on the atomic scale. Although numerous properties including eigenvalues and susceptibilities, of Hubbard clusters have been calculated previously, many open questions remain with regard to microscopic origins of charge-spin separation, pseudogap behavior, and various scenarios of possible pairings at low temperature. This chapter searches for transitions, over an extended parameter space that includes variations in chemical potential, magnetic field, Coulomb repulsion, and temperature. Insight into the properties of Hubbard clusters are gained by monitoring weak singularities in susceptibilities over this extended parameter space.

The effect of short-range correlations on the generalized momentum distribution in finite nuclei

The effect of dynamical short-range correlations on the generalized momentum distribution in the case of Z = N, ℓ-closed shell nuclei is investigated by introducing Jastrow-type correlations in the harmonic-oscillator model. First, a low-order approximation is considered and applied to the nucleus 4He. Compact analytical expressions are derived and numerical results are presented and the effect of centre-of-mass corrections is estimated. Next, an approximation is proposed for of heavier nuclei that uses the above-correlated of 4He. Results are presented for the nucleus 16O. It is found that the effect of short-range correlations is significant for rather large values of the momenta p and/or Q and should be included, along with centre-of-mass corrections for light nuclei, in a reliable evaluation of in the whole domain of p and Q.