Many-body Formalism Research Articles

Linked-Cluster Formulation of Electron-Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States.

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination, and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and time-dependent density functional theory (TDDFT) formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as many-body perturbation theory formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems, and results were found to be in good agreement with the EOM-CCSD and GW+BSE methods. The numerical results highlight the effectiveness of the developed method for overcoming the computational barrier of accurately determining the electron-hole interaction kernel to applications of large finite systems such as quantum dots and nanorods.

Erratum: Many-body formalism for thermally excited wave packets: A way to connect the quantum regime to the classical regime [Phys. Rev. A 95 , 062124 (2017)

Received 11 October 2017DOI:https://doi.org/10.1103/PhysRevA.96.049907©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum formalismQuantum statistical mechanicsQuantum-to-classical transitionTemperatureGeneral PhysicsCondensed Matter, Materials & Applied PhysicsStatistical Physics

Quantum field theory and the linguistic Minimalist Program: a remarkable isomorphism

By resorting to recent results, we show that an isomorphism exist between linguistic features of the Minimalist Program and the quantum field theory formalism of condensed matter physics. Specific linguistic features which admit a representation in terms of the many-body algebraic formalism are the unconstrained nature of recursive Merge, the operation of the Labeling Algorithm, the difference between pronounced and un-pronounced copies of elements in a sentence and the build-up of the Fibonacci sequence in the syntactic derivation of sentence structures. The collective dynamical nature of the formation process of Logical Forms leading to the individuation of the manifold of concepts and the computational self-consistency of languages are also discussed.

Many-body formalism for thermally excited wave packets: A way to connect the quantum regime to the classical regime

Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet operators that connects these two limits, the thermal energy being distributed between the state spatial extension and its thermal excitation. The corresponding `mixed quantum-classical' states, which render the Boltzmann operator diagonal, are the physically relevant states when the temperature is finite. The formulation of many-body Hamiltonians in terms of these thermally excited wave-packets and the resulting effective scatterings is provided.

Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of -spin electrons and -spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Δ, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons can end either in the same dark states with an amplitude , or in opposite-spin bright states , with a different amplitude , the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, , which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments.

Charge optimized many body (COMB) potentials for Pt and Au

Interatomic potentials for Pt and Au are developed within the third generation charge optimized many-body (COMB3) formalism. The potentials are capable of reproducing phase order, lattice constants, and elastic constants of Pt and Au systems as experimentally measured or calculated by density functional theory. We also fit defect formation energies, surface energies and stacking fault energies for Pt and Au metals. The resulting potentials are used to map a 2D contour of the gamma surface and simulate the tensile test of 16-grain polycrystalline Pt and Au structures at 300 K. The stress–strain behaviour is investigated and the primary slip systems {1 1 1}〈1 0〉 are identified. In addition, we perform high temperature (1800 K for Au and 2300 K for Pt) molecular dynamics simulations of 30 nm Pt and Au truncated octahedron nanoparticles and examine morphological changes of each particle. We further calculate the activation energy barrier for surface diffusion during simulations of several nanoseconds and report energies of eV for Pt and eV for Au. This initial parameterization and application of the Pt and Au potentials demonstrates a starting point for the extension of these potentials to multicomponent systems within the COMB3 framework.

Carrier capture in InGaN/GaN quantum wells: Role of electron-electron scattering

The competition of electron-electron interband scattering (ee) and longitudinal optical phonon emission (e-ph) as electron capture mechanisms is theoretically investigated in III-nitride quantum wells. The non-trivial separation of their scattering probabilities is discussed, and compact expressions for capture time are obtained in the framework of the quantum many-body formalism. At the typical operating conditions of light emitting diodes (LEDs), the model predicts an increasing importance of ee scattering as a capture mechanism with increasing carrier density. Verifications against recent experiments are presented to support this finding and confirm the need for population-dependent capture time expressions including both ee and e-ph mechanisms for an accurate description of LED carrier dynamics and efficiency.

Way to observe the implausible “trion-polariton”

Using the composite boson (coboson) many-body formalism, we determine under which conditions “trion-polariton” can exist. Dipolar attraction can bind an exciton and an electron into a trion having an energy well separated from the exciton energy. Yet, the existence of long-lived “trion-polariton” is a priori implausible not only because the photon-trion coupling, which scales as the inverse of the sample volume, is vanishingly small, but mostly because this coupling is intrinsically “weak”. Here, we show that a moderately dense Fermi sea renders its observation possible: on the pro side, the Fermi sea overcomes the weak coupling by pinning the photon to its momentum through Pauli blocking; it also overcomes the dramatically poor photon-trion coupling by providing a volume-linear trion subspace to which the photon is coherently coupled. On the con side, the Fermi sea broadens the photon-trion resonance due to the fermionic nature of trions and electrons; it also weakens the trion binding by blocking electronic states relevant for trion formation. As a result, the proper way to observe this novel polariton is to use a doped semiconductor having long-lived electronic states, a highly bound trion and a Fermi energy as large as a fraction of the trion binding energy.

Highly Magnetized Neutron Stars in a Many-body Forces Formalism

In this work, we study the effects of different magnetic field configurations in neutron stars described by a many-body forces formalism (MBF model). The MBF model is a relativistic mean field formalism that takes into account many-body forces by means of a meson field dependence of the nuclear interaction coupling constants. We choose the best parametrization of the model that reproduces nuclear matter properties at saturation and also describes massive neutron stars. We assume matter to be in beta-equilibrium, charge neutral and at zero temperature. Magnetic fields are taken into account both in the equation of state and in the structure of the stars by the self-consistent solution of the Einstein-Maxwell equations. We assume a poloidal magnetic field distribution and calculate its effects on neutron stars, showing its influence on the gravitational mass and deformation of the stars.

THE HYPERFINE STRUCTURE AND OSCILLATOR STRENGTHS PARAMETERS FOR SOME HEAVY ELEMENTS ATOMS AND IONS: REVIEW OF DATA BY RELATIVISTIC MANY-BODY PERTURBATION THEORY CALCULATION

The energies and hyperfine structure constants for some heavy Li-like multicharged ions are calculated within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. The magnetic inter-electron interaction is accounted for in the lowest order on a2 (a is the fine structure constant) parameter. The Lamb shift polarization part is taken into account in the modified Uehling-Serber approximation, the Lamb shift self-energy part - within the generalized Ivanov-Ivanova procedure. The combined relativistic energy approach and many-body perturbation theory with the zeroth order optimized one-particle approximation are used for computing the Li-like ions (Z=11-42,69,70) and Cs energies and oscillator strengths, in particular, of radiative transitions from the ground state to the lowexcited and Rydberg states 2s1/2 – np1/2,3/2, np1/2,3/2-nd3/2,5/2 (n=2-12) in the Li-like ions. A comparison of the calculated oscillator strengths with available theoretical and experimental data is performed.

Correlated-pair approach to composite-boson scattering lengths

We derive the scattering length of composite bosons (cobosons) within the framework of the composite boson many-body formalism that uses correlated-pair states as a basis, instead of free fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable, and that produce scattering lengths which match quantitatively well with the numerically-obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

Tuning the band gap and optical spectra of silicon-doped graphene: Many-body effects and excitonic states

In this work we carried out density functional theory calculations combined with many-body perturbation formalism to study the structural, electronic and optical properties of a monolayer graphene sheet doped with Si. The electronic properties are analyzed at three levels of many-body GW approach (G0W0, GW0 and GW) constructed over a Generalized Gradient Approximation functional. By substituting carbon atoms by silicon atoms on graphene, the band gap of these materials can be continuously tuned by changing the concentration of Si. The optical properties and excitonic effects in these materials are investigated using the Bethe-Salpeter equation approach. The exciton energies show that these materials can absorb the visible light, and that the absolute positions of the excitonic peaks depend on the Si concentration. The optical absorption spectra of the Si-doped graphene are dominated by bound Frenkel exciton and the silicon doping increases the optical conductivity of graphene in the visible range. These materials may be applied in photonic and optoelectronic devices such as solar cells and light-emitters.

Quasi-particle energies and optical excitations of ZnS monolayer honeycomb structure

Using ab-initio density functional theory calculations combined with many-body perturbation formalism we carried out the electronic structure and optical properties of 2D graphene-like ZnS structure. The electronic properties were analyzed at three levels of many-body GW approach (G0W0, GW0 and GW) constructed over a Generalized Gradient Approximation functional. Our results indicate that ZnS sheet has a direct band gap at the Γ-point. Also it is seen that inclusion of electron–electron interaction does not change the sort of direct semiconducting band gap in ZnS sheet. The optical properties and excitonic effects of these materials are investigated using the Bethe-Salpeter equation (BSE) approach. The formation of first exciton peaks at 3.86, 4.26, and 4.57eV with large binding energy of 0.36, 0.49 and 0.73eV using G0W0+BSE, GW0+BSE and GW+BSE, respectively, was observed. We show that the optical absorption spectrum of 2D ZnS structure is dominated by strongly bound Frenkel excitons. The enhanced excitonic effects in the ZnS monolayer sheet can be useful in designing optoelectronic applications.

Combining the Many-Body GW Formalism with Classical Polarizable Models: Insights on the Electronic Structure of Molecular Solids.

We present an original hybrid QM/MM scheme merging the many-body Green's function GW formalism with classical discrete polarizable models and its application to the paradigmatic case of a pentacene crystal. Our calculated transport gap is found to be in excellent agreement with reference periodic bulk GW calculations, together with properly parametrized classical microelectrostatic calculations, and with photoionization measurements at crystal surfaces. More importantly, we prove that the gap is insensitive to the partitioning of pentacene molecules in QM and MM subsystems, as a result of the mutual compensation of quantum and classical polarizabilities, clarifying the relation between polarization energy and delocalization. The proposed hybrid method offers a computationally attractive strategy to compute the full spectrum of charged excitations in complex molecular environments, accounting for both QM and MM contributions to the polarization energy, a crucial requirement in the limit of large QM subsystems.

Exploring Electrostatic Effects on the Hydrogen Bond Network of Liquid Water through Many-Body Molecular Dynamics.

To probe the dynamic nature of the hydrogen bond network in water, linear and nonlinear infrared spectra of dilute HOD in H2O are computed from many-body molecular dynamics simulations with the MB-pol potential, which have been shown to accurately predict the properties of water from the gas to the condensed phase. The effects of various approximations to the many-body expansion of the dipole moment surface on the OD-stretch absorption line shapes are analyzed at different levels of theory. The interplay between effects associated with the variation of the HOD dipole moment and instantaneous nuclear configurations causes qualitative differences in the absorption profiles, which are traced back to how induction contributions are treated within the many-body formalism. Further analysis of the multidimensional infrared spectra demonstrates that the spectral diffusion of the OD stretching frequencies depends explicitly on the level of truncation in the many-body expansion of the dipole moment in the short-time regime that is associated with intact hydrogen-bond dynamics. In contrast, the long-time evolution of spectral diffusion, describing collective rearrangements of the hydrogen-bond network, is effectively independent of the details with which many-body contributions to the dipole moment are represented.

Quasi-particle energies and optical excitations of wurtzite BeO and its nanosheet

The electronic and optical properties of BeO in wurtzite bulk and sheet structures are investigated by using ab-initio density functional theory calculations combined with many-body perturbation formalism. The electronic properties were analyzed at three levels of the many-body GW approach (G0W0, GW0 and GW) constructed over a Generalized Gradient Approximation functional. Our results show that GW approach does not change the sort of direct or indirect band gap in bulk or sheet systems of BeO. The best result for the insulating gap of the bulk system was obtained at the GW0 level. The optical properties and excitonic effects of these materials are investigated using the Bethe-Salpeter equation (BSE) approach. Comparison with experiment shows that the optical properties of the bulk system cannot be explained by independent-particle transitions but they are strongly dominated by excitonic effects. The binding energies of the first exciton for the bulk and sheet structures are 0.5 and 1.5 eV in E||x, respectively. The quantum confinement of BeO sheet significantly enhances the electron-hole interaction and finally leads to a larger binding energy. We show that the spectrum for both bulk and sheet systems is dominated by strongly bound Frenkel excitons.

Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach.

We have implemented the polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

Atomic motion from the mean square displacement in a monatomic liquid

V-T theory is constructed in the many-body Hamiltonian formulation, and is being developed as a novel approach to liquid dynamics theory. In this theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion, and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na, and find the motion evolves in three successive time intervals: on the first ‘vibrational’ interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second ‘crossover’ interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third ‘random walk’ interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. This motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.

Lattice expansion by intrinsic defects in uranium by molecular dynamics simulation

A re-formulated and re-parameterized interatomic potential for uranium metal in the Charge-Optimized Many-Body (COMB) formalism is presented. Most physical properties of the orthorhombic α and bcc γ phases are accurately reproduced. In particular, this potential can reproduce the negative thermal expansion of the b axis in α-U while keeping this phase as the most stable phase at low temperatures, in accord with experiment. Most of the volume expansion in α-U by intrinsic defects is shown to come from the b axis, due to the formation of prismatic loops normal to this direction. Glide dislocation loops forming stacking faults are also observed. Structures of both loop types are analyzed. An expansion simulation is conducted and the results are verified by using the Norgett-Robinson-Torrens model. Rather than forming extended defect structures as in α-U, the γ phase forms only isolated defects and thus results in a much smaller and isotropic expansion.

Many-body formalism for fermions: Testing the enforcement of the Pauli principle

Many-body formalism for fermions: Testing the enforcement of the Pauli principle