Electron-pair States Research Articles

Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions.

Wave functions based on electron-pair states provide inexpensive and reliable models to describe quantum many-body problems containing strongly correlated electrons, given that broken-pair states have been appropriately accounted for by, for instance, a posteriori corrections. In this article, we analyze the performance of electron-pair methods in predicting orbital-based correlation spectra. We focus on the (orbital-optimized) pair-coupled cluster doubles (pCCD) ansatz with a linearized coupled-cluster (LCC) correction. Specifically, we scrutinize how orbital-based entanglement and correlation measures can be determined from a pCCD-tailored CC wave function. Furthermore, we employ the single-orbital entropy, the orbital-pair mutual information, and the eigenvalue spectra of the two-orbital reduced density matrices to benchmark the performance of the LCC correction for the one-dimensional Hubbard model with the periodic boundary condition as well as the N2 and F2 molecules against density matrix renormalization group reference calculations. Our study indicates that pCCD-LCC accurately reproduces the orbital-pair correlation patterns in the weak correlation limit and for molecules close to their equilibrium structure. Hence, we can conclude that pCCD-LCC predicts reliable wave functions in this regime.

Measurement of the transverse momentum distribution of Drell\u2013Yan lepton pairs in proton\u2013proton collisions at sqrt{s}=13,TeV with the ATLAS detector

This paper describes precision measurements of the transverse momentum p_mathrm {T}^{ell ell } (ell =e,mu ) and of the angular variable phi ^{*}_{eta } distributions of Drell–Yan lepton pairs in a mass range of 66–116 GeV. The analysis uses data from 36.1 fb^{-1} of proton–proton collisions at a centre-of-mass energy of sqrt{s}=13,TeV collected by the ATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair and muon-pair final states are performed in the same fiducial volumes, corrected for detector effects, and combined. Compared to previous measurements in proton–proton collisions at sqrt{s}=7 and 8,TeV, these new measurements probe perturbative QCD at a higher centre-of-mass energy with a different composition of initial states. They reach a precision of 0.2% for the normalized spectra at low values of p_mathrm {T}^{ell ell }. The data are compared with different QCD predictions, where it is found that predictions based on resummation approaches can describe the full spectrum within uncertainties.

Gamma-ray spectra in the positron-annihilation process of molecules at room temperature

In this study, a fully self-consistent method was developed to obtain the wave functions of the positron and electrons in molecules simultaneously. The wave function of a positron at room temperature, with a characteristic energy of approximately 0.04 eV [1], was used to analyse the experimental results of its annihilation in helium, neon, hydrogen, and methane molecules. The interactions between the positron and molecule provide a significant correction in the gamma-ray spectra of the annihilating electron–positron pairs. It was also observed that high-order correlations offered almost no correction in the spectra, as the interaction between the low-energy positron and electrons cannot drive the electrons into excited electronic states. More accurate studies, which consider the coupling of the positron–electron pair states and vibration states of nuclei, must be undertaken.

Erratum: "Targeting excited states in all-trans polyenes with electron-pair states" [J. Chem. Phys. 145, 234105 (2016)

Erratum: "Targeting excited states in all-trans polyenes with electron-pair states" [J. Chem. Phys. 145, 234105 (2016)

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry.

Wave functions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this Article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allows us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multireference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori Linearized Coupled Cluster correction on top of AP1roG against CR-CC(2,3) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the homonuclear N2, C2, and F2 dimers as well as the heteronuclear BN, CO, and CN+ dimers against MRCI-SD, MRCI-SD+Q, and CR-CC(2,3) reference data. Our numerical results indicate that the best performance is obtained from a Linearized Coupled Cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG provide substantial improvements for binding energies and spectroscopic properties obtained with the AP1roG approach, while allowing us to approach chemical accuracy for reaction energies involving closed-shell species.

Targeting excited states in all-trans polyenes with electron-pair states

Wavefunctions restricted to electron pair states are promising models for strongly correlated systems. Specifically, the pair Coupled Cluster Doubles (pCCD) ansatz allows us to accurately describe bond dissociation processes and heavy-element containing compounds with multiple quasi-degenerate single-particle states. Here, we extend the pCCD method to model excited states using the equation of motion (EOM) formalism. As the cluster operator of pCCD is restricted to electron-pair excitations, EOM-pCCD allows us to target excited electron-pair states only. To model singly excited states within EOM-pCCD, we modify the configuration interaction ansatz of EOM-pCCD to contain also single excitations. Our proposed model represents a simple and cost-effective alternative to conventional EOM-CC methods to study singly excited electronic states. The performance of the excited state models is assessed against the lowest-lying excited states of the uranyl cation and the two lowest-lying excited states of all-trans polyenes. Our numerical results suggest that EOM-pCCD including single excitations is a good starting point to target singly excited states.

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

Wave functions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wave functions restricted to electron-pair states. We focus on the pair-coupled-cluster doubles (pCCD) ansatz also called the antisymmetric product of the 1-reference orbital geminal (AP1roG) method, combined with an orbital optimization protocol presented in Boguslawski et al. [Phys. Rev. B 89, 201106(R) (2014)], whose performance is assessed against electronic structures obtained form density-matrix renormalization-group reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with a periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of pCCD/AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information, as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the pCCD/AP1roG method. Furthermore, we examine the effect of orbital rotations within the pCCD/AP1roG model on correlations between orbital pairs.

Measurement of the transverse momentum and [Formula: see text] distributions of Drell-Yan lepton pairs in proton-proton collisions at [Formula: see text]TeV with the ATLAS detector.

Distributions of transverse momentum p_T^{ell ell } and the related angular variable phi ^*_eta of Drell–Yan lepton pairs are measured in 20.3 fb^{-1} of proton–proton collisions at sqrt{s}=8 TeV with the ATLAS detector at the LHC. Measurements in electron-pair and muon-pair final states are corrected for detector effects and combined. Compared to previous measurements in proton–proton collisions at sqrt{s}=7 TeV, these new measurements benefit from a larger data sample and improved control of systematic uncertainties. Measurements are performed in bins of lepton-pair mass above, around and below the Z-boson mass peak. The data are compared to predictions from perturbative and resummed QCD calculations. For values of phi ^*_eta < 1 the predictions from the Monte Carlo generator ResBos are generally consistent with the data within the theoretical uncertainties. However, at larger values of phi ^*_eta this is not the case. Monte Carlo generators based on the parton-shower approach are unable to describe the data over the full range of p_T^{ell ell } while the fixed-order prediction of Dynnlo falls below the data at high values of p_T^{ell ell }. ResBos and the parton-shower Monte Carlo generators provide a much better description of the evolution of the phi ^*_eta and p_T^{ell ell } distributions as a function of lepton-pair mass and rapidity than the basic shape of the data.

Hamiltonian of a many-electron system with single-electron and electron-pair states in a two-dimensional periodic potential

Based on the metastable electron-pair energy band in a two-dimensional (2D) periodic potential obtained previously by Hai and Castelano [J. Phys.: Condens. Matter 26, 115502 (2014)], we present in this work a Hamiltonian of many electrons consisting of single electrons and electron pairs in the 2D system. The electron-pair states are metastable of energies higher than those of the single-electron states at low electron density. We assume two different scenarios for the single-electron band. When it is considered as the lowest conduction band of a crystal, we compare the obtained Hamiltonian with the phenomenological model Hamiltonian of a boson-fermion mixture proposed by Friedberg and Lee [Phys. Rev. B 40, 6745 (1989)]. Single-electron-electron-pair and electron-pair-electron-pair interaction terms appear in our Hamiltonian and the interaction potentials can be determined from the electron-electron Coulomb interactions. When we consider the single-electron band as the highest valence band of a crystal, we show that holes in this valence band are important for stabilization of the electron-pair states in the system.

Metastable electron-pair states in a two-dimensional crystal

We study possible quantum states of two correlated electrons in a two-dimensional periodic potential and find a metastable energy band of electron pairs between the two lowest single-electron bands. These metastable states result from interplay of the electron–electron Coulomb interaction and the strength of the crystal potential. The paired electrons are bound in the same unit cell in relative coordinates with an average distance between them of approximately one third of the crystal period. Furthermore, we discuss how such electron pairs can possibly be stabilized in a many-electron system.

Magnetic and Vibronic Theory of the Influence of Ferroelectricity on Magnetic Properties of Bi-Based Multiferroics

It is shown that the electron-lattice covalent hybridization between the Bi 6s2 lone electron pair and empty oxygen 2p states causes instability of R25 and R15 polar vibrations in the reference cubic phase. The ferroelectric instability holds in the phase and the observed ferroelectric transition is connected with the softening of the A2u mode. We take into account vibronic couplings in the Bi-based multiferroics. We obtained the free energy of the Bi-based multiferroics taking into account the Zeeman splitting of electronic levels in an external magnetic field. On the base of the free energy we investigated the magnetoelectric effects in the Bi-based multiferroics.

Theory of ferroelectricity in Bi‐based multiferroics

AbstractAn electron‐phonon (vibronic) theory of the Bi‐based multiferroics is developed. It is shown that the electron‐lattice covalency hybridization between the Bi 6s2 lone electron pair and empty oxygen 2p states causes instability of R25 and R15 polar vibrations in the reference cubic phase. The cubic perovskite structure is distorted by displacements of oxygen ions corresponding to the condensation of the R25 mode at the boundary point R = π /a (1, 1, 1) of the Brillouin zone (a is the cell constant of the cubic phase). These oxygen displacements correspond to the rotation of the FeO6 octahedron in BiFeO3 about the cube space diagonal. The triply degenerate mode Γ1u participates in the s‐p mixing of Bi lone electron pair states and 2p oxygen states. The ferroelectric instability holds in the R $ \bar 3 $c phase and the observed ferroelectric transition R $ \bar 3 $c → R 3c is connected with the softening of the A2u mode. The Γ1u mode in the R $ \bar 3 $c phase splits in Eu and A2u modes. We have calculated the spontaneous polarization Ps = 30–40 μC/cm2 (Ps = 1.5 μC/cm2 is also possible), Tc = 1105 K and dielectric constants. It is shown that the phase transition of the first order is in agreement with the experiment. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

AN ELECTRON-PHONON THEORY OF THE Bi-BASED MAGNETIC-FERROELECTRIC PEROVSKITES

ABSTRACT It is shown that the electron-lattice covalency hybridization between the Bi 6s2 lone electron pair and empty oxygen 2p states causes instability of R25 and R15 polar vibrations in the reference cubic phase. The cubic perovskite structure is distorted by displacements of oxygen ions corresponding to the condensation of the R25 mode at the boundary point R=π/a(1, 1, 1) of the Brillouin zone (a is the cell constant). The ferroelectric instability holds in the phase and the observed ferroelectric transition is connected with the softening of the A2u mode. The Γ1u mode in the phase splits in Eu and A2u modes. We have calculated the spontaneous polarization Ps =30−40 μC/cm2 (Ps =1.5 μC/cm2 is also possible), Tc = 1105 K and dielectric constants.

From phase- to amplitude-fluctuation-driven superconductivity in systems with precursor pairing

The change-over from phase- to amplitude-fluctuation driven superconductivity is examined for a composite system of free electrons (Fermions with concentration n_F) and localized electron-pairs (hard-core Bosons with concentration n_B) as a function of doping-changing n_B. The coupling together of these two subsystems via a charge exchange term induces electron pairing below a certain T^* (showing up in form of a pseudogap) and ultimately superconductivity in the Fermionic subsystem. T^* steadily decreases with decreasing n_B. Below T^* this electron pairing leads to electron-pair resonant states (Cooperons) with quasi-particle features which strongly depend on $n_B$. For high concentrations, (n_B \simeq 0.5), correlation effects between the hard-core Bosons lead to itinerant Cooperons having a heavy mass m_p, but are long-lived. Upon reducing n_B, the mass as well as the lifetime of those Cooperons is considerably reduced. For high values of n_B, a superconducting state sets in at a T_c, being controlled by the phase stiffness D_\phi=\hbar^2 n_p/m_p of those Cooperons, where n_p denotes their density. Upon reducing n_B, the phase stiffness steadily increases, and eventually exceeds the pairing energy k_B T^*. The Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high T_c superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.

Pair-tunneling states in semiconductor quantum dots: Ground-state behavior in a magnetic field

Using classical mechanical and quantum Monte Carlo methods we trace the ground-state behavior with an applied magnetic field of localized electron pair states in a quantum dot. By developing a method to treat nonconserved paramagnetic interactions using variational and diffusion quantum Monte Carlo techniques we find (i) a single-triplet transition at very small magnetic field strengths, (ii) enhanced localization of the two electrons with increasing magnetic field, and (iii) a mechanism for pair breakup that is different from that proposed recently by Wan et al. [Phys. Rev. Lett. 75, 2879 (1995)].

Many-zone effects in cuprate superconductors

A new theoretical approach is proposed to study the states responsible for the superconductivity of crystals. Within the framework of the approach it is shown that in the electron-phonon system a class of new so-called coupled states arises. Electron-pair states with , postulated in the BCS method are included in this class in a natural manner. The model numerical calculations have shown that the SC gap depends on the number of bands crossing the Fermi level and on the momenta of interacting electrons and that the temperature dependence of the SC gap for HTSCs is more complicated (in agreement with the recent experimental data) than predicted in the BCS approach.

Many Band Effects in Cuprate Superconductors

The new theoretical approach is proposed for study the states responsible for superconductivity of crystals. Within the frameworks of worked out approach it is shown that in electron–phonon system a class of new so-called coupled states arises. Postulated in BCS method electron-pair states k1 + k2 = 0, s + s′ = 0 are in natural manner included in this class. The model numerical calculations have shown that SC gap depends on number of bands crossing the Fermi level on the momenta k1+k2 = K≠ 0 of interacting electrons and that the temperature dependence of SC gap for HTSC is more complicated (in agreement with the recent experimental data) then predicted in BCS approach.

On BCS theory of superconductivity in systems with overlapping bands I. Simple overlap

A generalisation of Nambu representation of electron-pair states permits, following simple laws of matrix algebra, a Green's function reformulation of Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity in systems with an arbitrary number ( N) of bands. Perceived inadequacies of the original Suhl-Matthias-Walker (SMW) formulation are reexamined. An energy symmetrization, which further simplifies the obtained mean-field Hamiltonian, is proposed. An approximate analytic solution of the resulting N × N determinantal equation yields an expression for T c( N) similar to that by Jha and Rajagopal in their N-layer theory, and BCS and SMW results are, in appropriate limits, recovered. A new band-energy condition, presently found to be important and consistent with experiment on the oxide ceramics, is trivially obtained. In multiband systems, where bands may cluster and lose individual identities, the obtained approximate equality of band energies is interpreted as analogous to similar equality of energies of k- and k′- electrons whose wave functions overlap, the latter being at the heart of the conventional BCS criterion. The connection between multiband and multilayer models is discussed.

Model of electronic processes in glassy semiconductors: Correlation with structural features

A model of electronic processes related to mobility gap states in glassy semiconductors is discussed. The electronic processes, as well as the gap states, are shown to be essentially correlated with structural features of glassy semiconductors. Spectral features of the gap states, first of all of electron and hole pair states with negative correlation energy, are considered for both slow and fast processes; the spectral characteristics, intrinsic for the material, are to be related to the gap width Eg. It is found that centres responsible for luminescence differ from those for photoinduced ESR and from centres controlling carrier transit and those for structural changes in the materials. Basic properties of the effects, including a plausible mechanism of the inverse Arrhenius law for luminescence quenching, are considered. Some predictions of the model are presented.

Contributions to Localization in the Silicon Inversion Layer from States in the Gap inSiOx

Recent experiments on silicon inversion layers in the activated conductivity regime have shown a variety of electronic behaviors which are in marked disagreement with the predictions of Mott-Anderson localization, which is due to random static-potential fluctuations. It is argued here that there is an additional mechanism causing electron localization which involves electron-pair states in the energy gap of the disordered oxide. It is shown that by including this mechanism it is possible to account for a variety of these electronic properties including the dependence of the mobility edge on electron density.