Self-energy Research Articles

Influence of Dimensional Quantization Effects on the Effective Mass of Major Charge Carriers in LED Heterostructures with InxGa1−xN/GaN Multiple Quantum Wells

By numerically solving the self-consistent system of the Schr¨odinger equations and Poisson electroneutrality, zone diagrams of LED heterostructures with InxGa1−xN/GaN multiple quantum wells have been calculated. The effect of electron–phonon interaction, nonparabolicity of the dispersion relation, and hybridization of the wave function on the values of the effective mass of major charge carriers in the InxGa1−xN/GaN quantum wells has been studied. The long-wave shift of 2D-plasmon resonances is associated with the temperature renormalization of the effective mass of two-dimensional carriers. To describe the temperature dependence of the effective mass, the function for the displacement of the 2D-plasmon resonance frequency is introduced.

Torsional regularization of self-energy and bare mass of electron

Abstract In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that torsion eliminates the ultraviolet divergence of the standard self-energy. We also show that the infrared divergence is absent. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: 0.4329 MeV , 90.95 MeV , and 1543 MeV , respectively. These values constitute about 85% of the observed, re-normalized masses.

Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches

We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.

Braided Scalar Quantum Field Theory

AbstractWe formulate scalar field theories in a curved braided ‐algebra formalism and analyse their correlation functions using Batalin–Vilkovisky quantization. We perform detailed calculations in cubic braided scalar field theory up to two‐loop order and three‐point multiplicity. The divergent tadpole contributions are eliminated by a suitable choice of central curvature for the ‐structure, and we confirm the absence of UV/IR mixing. The calculations of higher loop and higher multiplicity correlators in homological perturbation theory are facilitated by the introduction of a novel diagrammatic calculus. We derive an algebraic version of the Schwinger–Dyson equations based on the homological perturbation lemma, and use them to prove the braided Wick theorem.

Absorbing discretization effects with a massive renormalization scheme: The charm-quark mass

We present the first numerical implementation of the massive symmetric-momentum-subtraction (mSMOM) renormalization scheme and use it to calculate the charm-quark mass. Based on ensembles with three flavors of dynamical domain-wall fermions with lattice spacings in the range 0.11–0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretization effects than the SMOM scheme. Converting our results to the MS¯ scheme we obtain m¯c(3 GeV)=1.008(13) GeV and m¯c(m¯c)=1.292(12) GeV. Published by the American Physical Society 2024

Anomalous Frequency and Temperature Dependent Scattering in the Dilute Metallic Phase in Lightly Doped SrTiO_{3}.

The mechanism of superconductivity in materials with aborted ferroelectricity and its emergence out of a dilute metallic phase in systems like doped SrTiO_{3} is an outstanding issue in condensed matter physics. This dilute metal has anomalous properties that are both similar and different to those found in the normal state of other unconventional superconductors. For instance, T^{2} resistivity can be found at densities that are too small to allow current decay through electron-electron scattering. We have investigated the optical properties of the dilute metallic phase in doped SrTiO_{3} using THz time-domain spectroscopy. At low frequencies the THz response exhibits a Drude-like form as expected for typical metal-like conductivity. We observed the frequency and temperature dependencies to the low energy scattering rate Γ(ω,T)∝(ℏω)^{2}+(pπk_{B}T)^{2} expected in a conventional Fermi liquid. However, we find the lowest known p values of 0.39-0.72. As p is 2 in a canonical Fermi liquid and existing models based on energy dependent elastic scattering bound p from below to 1, our observation lies outside current explanation. Our data also give insight into the high temperature regime and show that the temperature dependence of the resistivity derives in part from strong T dependent mass renormalizations.

Derivation and analysis of the multichannel Dyson equation

Derivation and analysis of the multichannel Dyson equation

Erratum: Electron self-energy in QED at two loops revisited [Phys. Rev. D 98 , 113008 (2018)

Erratum: Electron self-energy in QED at two loops revisited [Phys. Rev. D <b>98</b> , 113008 (2018)

Tuning electronic and thermoelectric properties of armchair graphene nanoribbon in the presence of electron phonon coupling

Electronic and thermoelectric properties of armchair graphene nanoribbon taking into account the effects of interaction between electrons and Einstein phonons have been addressed. Specially we study the temperature dependence of thermal conductivity, density of states and specific heat of the structure. The effects of electron phonon coupling strength on thermal conductivity and thermoelectric electronic of the system have been studied. Green’s function method has been implemented to obtain electronic properties of the system in the context of Holstein Hamiltonian. One loop electronic self-energy of the Hamiltonian has been obtained in order to find interacting electronic Green’s function. The transport and thermoelectric properties of armchair graphene nanoribbon in the presence of electron phonon coupling can be readily found using interacting Green’s function based on Kubo formula. We find numerical results for chemical potential dependence of thermal conductivity and thermoelectric properties in the presence of Holstein phonons. Specially the behaviors of Seebeck coefficient, power factor function, figure of merit and Lorenz number of the system have been analyzed. Our results show turning on electron phonon coupling leads to reduction of band gap in density of states of the armchair nanoribbon.

Nonlinear Schwinger mechanism in QCD, and Fredholm alternatives theorem

We present a novel implementation of the Schwinger mechanism in QCD, which fixes uniquely the scale of the effective gluon mass scale and streamlines considerably the procedure of multiplicative renormalization. The key advantage of this method stems from the nonlinear nature of the dynamical equation that generates massless poles in the longitudinal sector of the three-gluon vertex. An exceptional feature of this approach is an extensive cancellation involving the components of the integral expression that determines the gluon mass scale; it is triggered once the Schwinger–Dyson equation of the pole-free part of the three-gluon vertex has been appropriately exploited. It turns out that this cancellation is driven by the so-called Fredholm alternatives theorem, which operates among the set of integral equations describing this system. Quite remarkably, in the linearized approximation this theorem enforces the exact masslessness of the gluon. Instead, the nonlinearity induced by the full treatment of the relevant kernel evades this theorem, allowing for the emergence of a nonvanishing mass scale. The numerical results obtained from the resulting equations are compatible with the lattice findings, and may be further refined through the inclusion of the remaining fundamental vertices of the theory.

Fluctuation-induced first order transition to collective motion

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

Resummation of local and non-local scalar self energies via the Schwinger–Dyson equation in de Sitter spacetime

Resummation of local and non-local scalar self energies via the Schwinger–Dyson equation in de Sitter spacetime

The chiral dependence of effective masses of polaron spin states in chiral structures

The renormalization of effective masses of polaron spin states in chiral structures is studied based on the direct spin–phonon coupling, in which the simple formulas for the renormalization of effective masses are derived for polarons with spin-up and spin-down states using a linear-combination operator method. The theoretical calculations show that the effective masses are renormalized significantly with increasing the cut-off wave vector of phonon modes and the renormalized magnitudes are different for right-handed and left-handed structures. Moreover, the renormalized magnitude for the spin-down state is larger than the spin-up one. This asymmetrical behavior naturally gives rise to very different conductivities for spin-up and spin-down states as electrons transmitted through the systems. These results not only enrich the microscopic origin of CISS mechanism, but also enlighten more experimental ways to explore CISS.

Improved Dielectric Response of Solids: Combining the Bethe-Salpeter Equation with the Random Phase Approximation.

The Bethe-Salpeter equation (BSE) can provide an accurate description of low-energy optical spectra of insulating crystals-even when excitonic effects are important. However, due to high computational costs it is only possible to include a few bands in the BSE Hamiltonian. As a consequence, the dielectric screening given by the real part of the dielectric function can be significantly underestimated by the BSE. Here, we show that universally accurate optical response functions can be obtained by combining a four-point BSE-like equation for the irreducible polarizability with a two-point Dyson equation that includes the higher-lying transitions within the random phase approximation. The new method is referred to as BSE+. It has a computational cost comparable to the BSE but a much faster convergence with respect to the size of the electron-hole basis. We use the method to calculate refractive indices and electron energy loss spectra for a test set of semiconductors and insulators. In all cases the BSE+ yields excellent agreement with experimental data across a wide frequency range and outperforms both the BSE and the random phase approximation.

Correlation Functions Involving Dirac Fields from Homotopy Algebras II: The Interacting Theory

Abstract We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum $A_{\infty }$ algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the same formula as in the previous paper holds in this case. We show that correlation functions from our formula satisfy the Schwinger–Dyson equations. We therefore confirm that correlation functions from our formula express correlation functions from the ordinary approach of quantum field theory.

Four-gluon vertex in collinear kinematics

To date, the four-gluon vertex is the least explored component of the QCD Lagrangian, mainly due to the vast proliferation of Lorentz and color structures required for its description. In this work we present a nonperturbative study of this vertex, based on the one-loop dressed Schwinger–Dyson equation obtained from the 4PI effective action. A vast simplification is brought about by resorting to “collinear” kinematics, where all momenta are parallel to each other, and by appealing to the charge conjugation symmetry in order to eliminate certain color structures. Out of the fifteen form factors that comprise the transversely-projected version of this vertex, two are singled out and studied in detail; the one associated with the classical tensorial structure is moderately suppressed in the infrared regime, while the other diverges logarithmically at the origin. Quite interestingly, both form factors display the property known as “planar degeneracy” at a rather high level of accuracy. With these results we construct an effective charge that quantifies the strength of the four-gluon interaction, and compare it with other vertex-derived charges from the gauge sector of QCD.

Exact classical approach to the electron's self-energy and anomalous g-factor

An exact classical approach to the calculation of electron's self-energy and anomalous g-factor is reported. The electron's intrinsic dynamics, related electrodynamics and occurrence of anomalous magnetic moment are completely determined. A unique regularization of the electromagnetic field scalar potential underlying all results is derived. A fundamental transcendental equation satisfied by the electron's anomalous g-factor is obtained, with solution , matching the experimentally measured value reported in the literature to 0.59 parts per trillion. Field representation of the electron intrinsic and orbital dynamics in atoms is discussed.

Schwinger–Dyson Equation on the Complex Plane: A Four-Fermion Interaction Model at Finite Temperature

Abstract We extend the Schwinger–Dyson equation (SDE) on the complex plane, which was treated in our previous research, to finite temperature. As a simple example, we solve the SDE for a model with four-fermion interactions in (1+1) space-time dimensions in the strong coupling region. We investigate the properties of the effective mass and energy for the fermions, especially near the phase transition temperature.

Strebel Differentials and String Field Theory

Abstract A closed string worldsheet of genus g with n punctures can be presented as a contact interaction in which n semi-infinite cylinders are glued together in a specific way via the Strebel differential on it, if $n\ge 1,\ 2g-2+n\gt 0$. We construct a string field theory of closed strings such that all the Feynman diagrams are represented by such contact interactions. In order to do so, we define off-shell amplitudes in the underlying string theory using the combinatorial Fenchel–Nielsen coordinates to describe the moduli space and derive a recursion relation satisfied by them. Utilizing the Fokker–Planck formalism, we construct a string field theory from which the recursion relation can be deduced through the Schwinger–Dyson equation. The Fokker–Planck Hamiltonian consists of kinetic terms and three-string interaction terms.

Impact of Electron-Phonon Coupling on Graphene Intercalation Compounds from Self Energy: Polynomial Models Selection

In our pursuit of understanding electron-phonon coupling (EPC) and their impact on material properties, we delved deep into the intricate role played by the Eliashberg function in governing electron self-energy. Through meticulous evaluation of tailored polynomial models approximating this function, we unearthed profound insights into how phonon interactions intricately modify electronic energy bands. Employing numerical computations, we meticulously unraveled both the real and imaginary aspects of electron self-energy, crucial in comprehending EPC effects in various materials. Investigating superconductivity within monolayer graphene and its interaction with diverse doping substances, our study led us to identify optimal polynomial models that accurately capture EPC behaviors, offering invaluable implications for predicting critical temperatures in superconducting materials. Expanding the parameters within our models allowed us to anticipate changes in self-energy models for higher-order configurations not explored in this study. Our selection of polynomial spanning degrees from n = 1 to 10 the efficacy of n = 2 (Debye) as the most realistic and accurate model, closely followed by n = 1, albeit occasional deviations observed in specific materials. These discrepancies often stemmed from noise model inaccuracies and parameter approximations. Our comprehensive approach outshone the traditional Kramer-Kronig transform in assessing electron-phonon interactions. Looking ahead, the application of multiple models to the Eliashberg function diagram holds immense promise for enhancing accuracy, despite the challenge of concurrently adjusting multiple input parameters. This integration of numerical modeling with experimental data forms a robust framework, empowering the prediction and fine-tuning of material properties vital for the future fabrication of devices. HIGHLIGHTS Exploring the use of polynomial models to approximate the Eliashberg function, enabling a detailed analysis of electron-phonon coupling (EPC) in materials. Confirm the Debye model's accuracy in predicting the electronic structure of doped graphene. The findings suggest enhanced EPC in materials like CaC6 and its potential to induce superconductivity in monolayer graphene. This work offers a framework for future research and applications in superconducting materials using ARPES data. GRAPHICAL ABSTRACT