Self-energy Contributions Research Articles

Convergence-acceleration approach to partial-wave expansion of two-electron self-energy contributions to the Lamb shift

Convergence-acceleration approach to partial-wave expansion of two-electron self-energy contributions to the Lamb shift

Kinetic theory for spin-polarized relativistic plasmas

The investigation of spin and polarization effects in ultra-high intensity laser–plasma and laser–beam interactions has become an emergent topic in high-field science recently. In this paper, we derive a relativistic kinetic description of spin-polarized plasmas, where quantum-electrodynamics effects are taken into account via Boltzmann-type collision operators under the local constant field approximation. The emergence of anomalous precession is derived from one-loop self-energy contributions in a strong background field. We are interested, in particular, in the interplay between radiation reaction effects and the spin polarization of the radiating particles. For this, we derive equations for spin-polarized quantum radiation reaction from moments of the spin-polarized kinetic equations. By comparing with the classical theory, we identify and discuss the spin-dependent radiation reaction terms and radiative contributions to spin dynamics.

Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles.

Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a nonperturbative, self-consistent description of strongly coupled molecular ensembles, taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated intermolecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

Magnetized matter effects on dilaton photon mixing

Dilatons [$\ensuremath{\phi}(x)$] are a class of bosonic scalar particles associated with scaling symmetry and its compensation (under the violations of the same). They are capable of interacting gravitationally with other massive bodies. As they have coupling to two photons ($\ensuremath{\gamma}$), they are (also) capable of decaying to the two photons. However, the decay time is long and that makes them a good candidate for dark matter. Furthermore due to two photon coupling, they can produce optical signatures in a magnetic field. In a vacuum or plain matter they couple to one of the transversely polarized states of the photon. But in magnetized matter, they couple to both the transversely polarized state of photons (due to the emergence of a parity violating part of the photon self-energy contribution from magnetized matter). Being spin zero scalar, they could mix with spin zero longitudinal part of photons but they do not. A part of this work is directed towards understanding this issue of mixing the scalar with various polarization states of photons in a medium (magnetized or unmagnetized) due to the constraints from different discrete symmetries, e.g., charge conjugation ($\mathbf{C}$), parity ($\mathbf{P}$) and time reversal ($\mathbf{T}$) associated with the interaction. Based on these symmetry aided arguments, the structure of the mixing matrix is found to be $3\ifmmode\times\else\texttimes\fi{}3$, as in the case of neutrino flavor mixing matrix. Thus there exists nonzero finite probabilities of oscillation between different polarization states of photon to dilaton. Our analytical and numerical analysis show no existence of periodic oscillation length either in temporal or spatial direction for the most general values of the parameters in the theory. Possible astrophysical consequences of these results can be detected through the discussed observations.

On self-energy contributions near Berezinskii–Kosterlitz–Thouless transition in interacting homogeneous 2D Bose system

ABSTRACT We explore the consequences of including quantum corrections in an interacting 2D Bose system near Berezinskii–Kosterlitz–Thouless (BKT) transition. To go beyond mean-field theory and treat correlations, we use Matsubara Green's function method, and, following a previous novel approach, study features of the interacting Green's function just above the transition. We numerically obtain self-consistent solutions of boson self-energy to second order as well as higher order (re-summation of ladder and bubble diagrams) in the interaction strength, for the entire range of momentum, k, and compare our findings with analytic results in the limits of low- and high-k. Thereby, in the weak interaction limit, we retrieve the universal transition condition and calculate the universal scaling parameter (independent of interaction strength). The renormalised single-particle Green's function is found to decay algebraically at large distance r.

Leptogenesis in an extended seesaw model with U(1) B−L symmetry

We have explored an extended seesaw model accommodating a keV sterile neutrino adopting U(1) B−L symmetry. This model provides a natural platform for achieving resonant leptogenesis to account for the observed baryon asymmetry of the Universe (BAU). The required lepton asymmetry is sourced by the CP violating decay of the lightest heavy right-handed neutrino to Standard Model leptons and Higgs. The presence of the light sterile neutrino in the model brings out an enhancement in the final lepton asymmetry through an additional self-energy contribution. Adopting a proper treatment for all the washout processes this framework strictly favors a strong washout regime thereby protecting the low energy neutrino mass parameters in agreement with the present neutrino and cosmology data. This framework of extended seesaw scheme offers the source of matter–antimatter asymmetry without any severe fine-tuning of the Yukawa couplings governing the tiny neutrino mass. We also comment on the half-life period for the neutrinoless double beta decay process in the background of having a keV sterile neutrino satisfying all the constraints which guide the explanation for the observed BAU.

Shear induced polarization: collisional contributions

It has been realized that thermal shear plays a similar role as thermal vorticity in polarizing spin of particles in heavy ion collisions. We point out that shear has a funda- mental difference that it leads to particle redistribution in the medium. The redistribution gives rise to an additional contribution to spin polarization through the self-energy, which is parametrically the same order as the one considered so far in the literature. The self-energy contribution is in general gauge dependent. We introduce double gauge links stretching along the Schwinger-Keldysh contour to restore gauge invariance. We also generalize the straight path to adapt to the Schwinger-Keldysh contour. We find another contribution associated with the gauge link, which is also parametrically the same order. We illustrate the two contributions with a massive probe fermion in massless QED plasma with shear. A modest suppression of spin polarization is found from the combined contributions when the probe fermion has momentum much greater than the temperature.

Beta-borophene under the circularly polarized radiation: polaritonic and polaronic dynamic band structure

We study the effect of circularly polarized electromagnetic radiation on the optical polarons in a monolayer \({\beta}\)-borophene. We focus our attention on the off-resonant regime of large driving frequencies, which allows us to set up an effectively time-independent Hamiltonian describing the radiation field up to the second perturbational order. The contributions of optical surface phonons are incorporated according to the Lee–Low–Pines theory, via a sequence of appropriate unitary transformations. A central object in our investigation is the electronic band gap, which is shown to be widely controllable via the variation of light irradiation and substrate properties. We also show that the polaron self-energy contribution gives more contribution than the combination of the polaronic and polaritonic effects.

Electron self-energy corrections using the Welton concept for atomic structure calculations

The high level of accuracy achieved by atomic experiments in recent time has shone a spotlight on the need for a similarly high level of accuracy in atomic structure calculations, and in particular, QED prediction. A method of electron self-energy correction originally derived from the Welton idea by Lowe et al. (2013) (LCG-Welton method) has now been fully incorporated into the popular atomic structural package, GRASP2K, which we have introduced in this paper. A series of benchmark tests and results are presented, which enables the comparison of the implementations of different versions of GRASP2K, and the implementations on different platforms or operating systems. Test results presented in this paper demonstrate that these new implementations maintain the overall consistency and stability of the program across various platforms, while at the same time improve the accuracy of final energies. Our calculations for hydrogenic Lyα1,2 transitions show excellent agreement with experiment, to within less than 0.5 eV. On helium-like systems, our calculations show an improvement from the previous GRASP2K screening method. The new results from electronic self-energy contribution using the LCG-Welton method is more consistent with current standards in the literature, where they now fit within experimental variability of up to 0.1 eV. An option for users to adjust the gauge factor in the electric component of the transition rate has also been added to facilitate further investigation of this particular topic.

4-component relativistic Hamiltonian with effective QED potentials for molecular calculations.

We report the implementation of effective quantum electrodynamics (QED) potentials for all-electron four-component relativistic molecular calculations using the DIRAC code. The potentials are also available for two-component calculations, being properly picture-change transformed. The latter point is important; we demonstrate through atomic calculations that picture-change errors are sizable. Specifically, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48, 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykkö and L.-B. Zhao, J. Phys. B: At., Mol. Opt. Phys. 36, 1469 (2003) and V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005)] for electron self-energy. We provide extensive theoretical background for these potentials, hopefully reaching an audience beyond QED specialists. We report the following sample applications: (i) We first confirm the conjecture of P. Pyykkö that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants B0 of the three isotopomers studied by microwave spectroscopy; QED brings the corresponding substitution Au-C bond length rs from 0.23 to 0.04pm agreement with experiment. (ii) In regard to spectroscopic constants of van der Waals dimers M2 (M = Hg, Rn, Cn, Og), QED induces bond length expansions on the order of 0.15(0.30) pm for row 6(7) dimers. (iii) We confirm that there is a significant change of valence s population of Pb in the reaction PbH4 → PbH2 + H2, which is thereby a good candidate for observing QED effects in chemical reactions, as proposed in [K. G. Dyall et al., Chem. Phys. Lett. 348, 497 (2001)]. We also find that whereas in PbH4 the valence 6s1/2 population resides in bonding orbitals, it is mainly found in nonbonding orbitals in PbH2. QED contributes 0.32 kcal/mol to the reaction energy, thereby reducing its magnitude by -1.27%. For corresponding hydrides of superheavy flerovium, the electronic structures are quite similar. Interestingly, the QED contribution to the reaction energy is of quite similar magnitude (0.35 kcal/mol), whereas the relative change is significantly smaller (-0.50%). This curious observation can be explained by the faster increase in negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge.

Tuning of nonlinear optical properties by size and photonic intensity in CdS/ZnSe core/shell quantum dot-matrix pattern

In this work, we perform a theoretical analysis of the electronic and optical properties of CdS quantum dot (QD) encapsulated in ZnSe matrix. The intersubband energy levels and the matching wave functions are calculated using the effective mass approximation (E.M.A) and the compact density matrix approach. The effect of self-energy contribution due to the charging of CdS QD with ZnSe matrix has been taken into account from the beginning. We found that the linear and nonlinear optical properties are considerably impacted by the size parameter and the optical intensity I. The results obtained have essential consequences for the design of optoelectronic and photonic devices.

Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ increases by about $10$\% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.

Assessing the G0W0Γ0(1) Approach: Beyond G0W0 with Hedin's Full Second-Order Self-Energy Contribution.

We present and benchmark a self-energy approach for quasiparticle energy calculations that goes beyond Hedin's GW approximation by adding the full second-order self-energy (FSOS-W) contribution. The FSOS-W diagram involves two screened Coulomb interaction (W) lines, and adding the FSOS-W to the GW self-energy can be interpreted as first-order vertex correction to GW (GWΓ(1)). Our FSOS-W implementation is based on the resolution-of-identity technique and exhibits better than O(N5) scaling with system size for small- to medium-sized molecules. We then present one-shot GWΓ(1) (G0W0Γ0(1)) benchmarks for the GW100 test set and a set of 24 acceptor molecules. For semilocal or hybrid density functional theory starting points, G0W0Γ0(1) systematically outperforms G0W0 for the first vertical ionization potentials and electron affinities of both test sets. Finally, we demonstrate that a static FSOS-W self-energy significantly underestimates the quasiparticle energies.

Ground state properties and infrared spectra of anharmonic vibrational polaritons of small molecules in cavities.

Recent experiments and theory suggest that ground state properties and reactivity of molecules can be modified when placed inside a nanoscale cavity, giving rise to strong coupling between vibrational modes and the quantized cavity field. This is commonly thought to be caused either by a cavity-distorted Born-Oppenheimer ground state potential or by the formation of light-matter hybrid states, vibrational polaritons. Here, we systematically study the effect of a cavity on ground state properties and infrared spectra of single molecules, considering vibration-cavity coupling strengths from zero up to the vibrational ultrastrong coupling regime. Using single-mode models for Li-H and O-H stretch modes and for the NH3 inversion mode, respectively, a single cavity mode in resonance with vibrational transitions is coupled to position-dependent molecular dipole functions. We address the influence of the cavity mode on polariton ground state energies, equilibrium bond lengths, dissociation energies, activation energies for isomerization, and on vibro-polaritonic infrared spectra. In agreement with earlier work, we observe all mentioned properties being strongly affected by the cavity, but only if the dipole self-energy contribution in the interaction Hamiltonian is neglected. When this term is included, these properties do not depend significantly on the coupling anymore. Vibro-polaritonic infrared spectra, in contrast, are always affected by the cavity mode due to the formation of excited vibrational polaritons. It is argued that the quantized nature of vibrational polaritons is key to not only interpreting molecular spectra in cavities but also understanding the experimentally observed modification of molecular reactivity in cavities.

Repulsive Casimir–Lifshitz pressure in closed cavities

We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the self-energy contribution to the pressure tend to expand the sphere.

Self-induction and magnetic effects in electron transport through a photon cavity

We explore higher order dynamical effects in the transport through a two-dimensional nanoscale electron system embedded in a three-dimensional far-infrared photon cavity. The nanoscale system is considered to be a short quantum wire with a single circular quantum dot defined in a GaAs heterostructure. The whole system, the external leads and the central system are placed in a constant perpendicular magnetic field. The Coulomb interaction of the electrons, the para- and diamagnetic electron-photon interactions are all treated by a numerically exact diagonalization using step-wise truncations of the appropriate many-body Fock spaces. We focus on the difference in transport properties between a description within an electric dipole approximation and a description including all higher order terms in a single photon mode model. We find small effects mostly caused by an electrical quadrupole and a magnetic dipole terms that depend strongly on the polarization of the cavity field with respect to the transport direction and the photon energy. When the polarization is aligned along the transport direction we find indications of a weak self-induction that we analyze and compare to the classical counterpart, and the self-energy contribution of high-order interaction terms to the states the electrons cascade through on their way through the system. Like expected the electron-photon interaction is well described in the dipole approximation when it is augmented by the lowest order diamagnetic part for a nanoscale system in a cavity in an external magnetic field.

QED interaction effects on heavy meson masses from lattice QCD+QED

Hadron masses are subject to few MeV corrections arising from QED interactions, almost entirely arising from the electric charge of the valence quarks. The QED effects include both self-energy contributions and interactions between the valence quarks/antiquarks. By combining results from different signs of the valence quark electric charge we are able to isolate the interaction term which is dominated by the Coulomb piece, $⟨{\ensuremath{\alpha}}_{\mathrm{QED}}{e}_{{q}_{1}}{e}_{{\overline{q}}_{2}}/r⟩$, in the nonrelativistic limit. We study this for ${D}_{s}$, ${\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}$ mesons, working in lattice QCD plus quenched QED. We use gluon field configurations that include up, down, strange and charm quarks in the sea at multiple values of the lattice spacing. Our results, including also values for mesons with quarks heavier than charm, can be used to improve phenomenological models for the QED contributions. The QED interaction term carries information about meson structure; we derive effective sizes $⟨1/{r}_{\mathrm{eff}}{⟩}^{\ensuremath{-}1}$ for ${\ensuremath{\eta}}_{c}$, $J/\ensuremath{\psi}$ and ${D}_{s}$ of 0.206(8) fm, 0.321(14) fm and 0.307(31) fm respectively.

Higher-order logarithmic corrections and the two-loop self-energy of a 1s electron in hydrogen

The leading computational QED uncertainty of the Lamb shift in the $1s$ state in the hydrogen atom and helium ion is due to two-loop pure self-energy contributions. An exact evaluation in $Z\ensuremath{\alpha}$ has not yet been performed for $Z=1,2$, while a calculation based on the $Z\ensuremath{\alpha}$ expansion has a limited accuracy. To improve it, we calculate a leading logarithmic contribution in order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{8}m$ and estimate the nonleading subterms in orders ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{7}m$ and ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{8}m$. To further improve the accuracy, we take advantage of a combined evaluation of the numerical results of the exact calculations in $Z\ensuremath{\alpha}$ performed at $Z=10--30$, and the results of the $Z\ensuremath{\alpha}$ expansion in order to reach the most accurate result, which can be done by fitting the data. The quality of the fit, including its reliability and accuracy, strongly depends on a theoretical input, which is the main target of this paper. Strictly speaking, we develop not a fit, but a theoretical approximation for the pure self-energy contribution, which may serve as a base for a robust fit. It is also important to estimate a deviation of the truncated function from the true one. For this purpose, we calculate the leading logarithmic term and estimate the subleading ones in order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{9}m$. That allows us to find a reliable result which is more accurate than both fits over the numerical data and the results from the $Z\ensuremath{\alpha}$ expansion, which have been previously considered in literature. Performing the fit procedures, we focus our attention on the theoretical input which plays an essential role in the reliability and accuracy of the fit. Our results for the two-loop pure self-energy contribution to the $1s$ Lamb shift are expressed in a standard notation as ${B}_{60}=\ensuremath{-}72(7),\phantom{\rule{0.28em}{0ex}}{G}_{60}(Z=1)=\ensuremath{-}80(6)$, and ${G}_{60}(Z=2)=\ensuremath{-}83(5)$. That significantly improves the theoretical accuracy of the $1s$ Lamb shift in hydrogen, deuterium, and in the helium ions.

Hubbard model on a triangular lattice: Pseudogap due to spin density wave fluctuations

We calculate the fermionic spectral function $A_k (\omega)$ in the spiral spin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature $T$. The spiral SDW order $\Delta (T)$ develops below $T = T_N$ and has momentum ${ \bf K} = (4\pi/3,0)$. We pay special attention to fermions with momenta ${\bf k}$, for which ${\bf k}$ and ${\bf k} + {\bf K}$ are close to Fermi surface in the absence of SDW. At the mean field level, $A_k (\omega)$ for such fermions has peaks at $\omega = \pm \Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at $T > T_N$. We show that this behavior changes qualitatively beyond mean-field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a non-perturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that $A_k (\omega)$ shows peak/dip/hump features at $T < T_N$, with the peak position at $\Delta (T)$ and hump position at $\Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p > T_N$, and in between $T_N$ and $T_p$ the spectral function displays the pseudogap behavior. We show that the difference between $T_p$ and $T_N$ is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, $T_p = T_N$, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.

QED radiative corrections to the P1/22−P3/22 fine structure in fluorinelike ions

Ab initio calculations of QED radiative corrections to the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure transition energy are performed for selected F-like ions. These calculations are nonperturbative in $\alpha Z$ and include all first-order and many-electron second-order effects in $\alpha$. When compared to approximate QED computations, a notable discrepancy is found especially for F-like uranium for which the predicted self-energy contributions even differ in sign. Moreover, all deviations between theory and experiment for the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure energies of F-like ions, reported recently by Li et al., Phys. Rev. A 98, 020502(R) (2018), are resolved if their highly accurate, non-QED fine-structure values are combined with the QED corrections ab initially evaluated here.