Vertex Corrections Research Articles

Strong connection between single-particle and density excitations in Bose–Einstein condensates

Strong connection between the single-particle excitation and the collective excitation stands out as one of the features of Bose–Einstein condensates (BECs). We discuss theoretically these single-particle and density excitations of BECs focusing on the exact properties of the one-body and two-body Green’s functions developed by Gavoret and Nozières. We also investigate these excitations by using the many-body approximation theory at nonzero temperatures. First, we revisited the earlier study presented by Gavoret and Nozières, involving the subsequent results given by Nepomnyashchii and Nepomnyashchii, in terms of the matrix formalism representation. This matrix formalism is an extension of the Nambu representation for the single-particle Green’s function of BECs to discuss the density and current response functions efficiently. We describe the exact low-energy properties of the correlation functions and the vertex functions, and discuss the correspondence of the spectra between the single-particle excitation and the density excitation in the low-energy and low-momentum limits at T = 0. After deriving the exact low-energy structures of the one-body and two-body Green’s functions, we develop a many-body approximation theory of BECs with making the use of the matrix formalism for describing the single-particle Green’s function and the density response function at nonzero temperatures. We show how the peaks of the single-particle spectral function and the density response function behave with an increasing temperature. Many-body effect on the single-particle spectral function and the density response function is included within a random phase approximation, where satellite structures emerge because of beyond-mean-field effects. Criticisms are also made on recent theories casting doubt upon the conventional wisdom of the BEC: the equivalence of the dispersion relations between the single-particle excitation and the collective excitation in the low-energy and low-momentum regime.

Nonperturbative renormalization of the interaction of quantum dots with the phonon reservoir

The quantum dynamics of a single quantum dot with phonon reservoir is investigated by making use generalized quantum dynamics equation [Gainutdinov R.Kh. 1999 J. Phys. A 32 5675]. The self-energy function is calculated nonperturbatively taking into account the renormalization of the vertex function. In this paper, we show that the nonperturbative renormalization of the vertex function significantly affects the nature of the interaction of the quantum dot with the phonon reservoir.

Stuckelberg SUSY QED and infrared problem

We review gauge invariant [Formula: see text] supersymmetric massive U(1) gauge theory coupled to matter and Stuckelberg superfields. We focus on the leading order self-energy and vertex correction to the matter field in the massless limit of both the U(1) vector superfield and the Stuckelberg superfield. We explicitly verify that the theory is infrared divergence free in the massless limit. Hence the Stuckelberg mechanism appears to be the efficient route to handle infrared divergences seen in supersymmetric quantum electrodynamics. Since these additional particles have very small masses they can serve as dark matter candidates through “Ultralight particles” mechanism.

Charge transport in the Hubbard model at high temperatures: Triangular versus square lattice

High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory (DMFT) and its cluster extensions, as well as the finite-temperature Lanczos method (FTLM) to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattice at half-filling and at 15\% hole-doping. We find that for $T \gtrsim 1.5t$ the self-energy becomes practically local, while the finite-size effects become small at lattice-size $4 \times 4$ for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.

Dynamic response functions of two-dimensional Dirac fermions with screened Coulomb and short-range interactions

We consider a screened Coulomb interaction between electrons in graphene and determine their dynamic response functions, such as a longitudinal and a transverse electric conductivity and a polarization function and compare them to the corresponding quantities in the short-range interaction model. The calculations are performed to all orders for short-range interaction by taking into account the self-energy renormalization of the electron velocity and using a ladder approximation to account for the vertex corrections, ensuring that the Ward identity (charge conservation law) is satisfied. Our findings predict a resonant response of interacting electron-hole pairs at a particular frequency below the threshold $qv=\omega$ and further predict an instability for sufficiently strong interactions.

Elastic α−C12 scattering at low energies with the sharp resonant 03+ state of O16

An inclusion of sharp resonant $0_3^+$ state of $^{16}$O and first excited $2_1^+$ state of $^{12}$C in a study of $s$-wave elastic $\alpha$-$^{12}$C scattering at low energies is investigated in an effective Lagrangian approach. The elastic scattering amplitude is parted into two; one is for the sharp resonant $0_3^+$ state of $^{16}$O parameterized by Breit-Wigner formula, and the other is for a non-resonant part of the amplitude parameterized by effective range expansion. In the non-resonant part of the amplitude, a contribution from the $2_1^+$ state of $^{12}$C is included. We discuss a large correlation between a coupling for the $2_1^+$ state of $^{12}$C and an effective range parameter $Q_0$ as well as a necessity of inclusion of a vertex correction for the initial and final $\alpha$-$^{12}$C states. After fixing parameters appearing in the amplitudes by using experimental data, we calculate asymptotic normalization coefficients for ground $0_1^+$ state and first excited $0_2^+$ state of $^{16}$O and compare them to previous results found in literature.

A non-iterative method for vertex corrections of the Kubo formula for electric conductivity

When computing electric conductivity based on the Kubo formula, vertex corrections describe such effects as anisotropic scattering and quantum interference and are important in determining quantum transport properties. These vertex corrections are obtained by solving the Bethe–Salpeter equation, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to vertex correction based on rank factorization of the impurity vertices, which significantly alleviates the computational burden. We demonstrate that this method can be implemented along with effective Hamiltonians extracted from electronic structure calculations on perfect crystals, thereby enabling the quantitative analysis of quantum effects in electron conduction for real materials.

Study of finite fermionic chains with edge modes using an appropriate momentum representation

This work is based on the Su-Schrieffer-Heeger model, which describes a system of non-interacting polarized fermions, i.e. without spin, moving in a one-dimensional optical superlattice with fixed boundary conditions. Starting from the Hamiltonian of the system in second quantization, in which the optical lattice has discretized the space, and taking into account that the basis that diagonalizes the kinetic energy is the one of momentum, we perform the discrete sine transform type-I, which respects the hard-wall boundary conditions of the system and allows us to expressour Hamiltonian in the momentum basis, in such a way that we can think that it is possible to extend the study to an arbitrary number of sites. Finally we apply the Bogoliubov-de Gennes formalism getting the dispersion relation and the bare vertex function where together they form the couplings matrix. By diagonalizing this matrix, we visualize the parameter set where the system hosts zero energy modes.

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.

Doping effects on electronic states in electron-doped FeSe: Impact of self-energy and vertex corrections

The pairing glue of high-$T_{\rm c}$ superconductivity in heavily electron-doped (e-doped) FeSe, in which hole-pockets are absent, has been an important unsolved problem. Here, we focus on a heavily e-doped bulk superconductor Li$_{1-x}$Fe$_x$OHFeSe ($T_{\rm c} \sim 40$K). We construct a multiorbital model beyond the rigid band approximation and analyze the spin and orbital fluctuations by taking both vertex corrections (VCs) and self-energy into consideration. Without e-doping ($x=0$), the ferro-orbital order without magnetism in FeSe is reproduced by the VCs.The orbital order quickly disappears when the hole-pocket vanishes at $x \sim 0.03$. With increasing $x$ further, the spin fluctuations remain small, whereas orbital fluctuations gradually increase with $x$ due to the VCs. The negative feedback due to the self-energy is crucial to explain experimental phase diagram. Thanks to both vertex and self-energy corrections, the orbital-fluctuation-mediated $s_{++}$-wave state appears for a wide doping range, consistent with experiments.

Nonadiabatic superconductivity in a Li-intercalated hexagonal boron nitride bilayer.

When considering a Li-intercalated hexagonal boron nitride bilayer (Li-hBN), the vertex corrections of electron–phonon interaction cannot be omitted. This is evidenced by the very high value of the ratio λωD/εF ≈ 0.46, where λ is the electron–phonon coupling constant, ωD is the Debye frequency, and εF represents the Fermi energy. Due to nonadiabatic effects, the phonon–induced superconducting state in Li-hBN is characterized by much lower values of the critical temperature (TLOVCC ∈ {19.1, 15.5, 11.8} K, for μ* ∈ {0.1, 0.14, 0.2}, respectively) than would result from calculations not taking this effect into account (TMEC∈ {31.9, 26.9, 21} K). From the technological point of view, the low value of TC limits the possible applications of Li-hBN. The calculations were carried out under the classic Migdal–Eliashberg formalism (ME) and the Eliashberg theory with lowest-order vertex corrections (LOVC). We show that the vertex corrections of higher order (λ3) lower the value of TLOVCC by a few percent.

High-frequency asymptotics of the vertex function: Diagrammatic parametrization and algorithmic implementation

Vertex functions are a crucial ingredient of several forefront many-body algorithms in condensed matter physics. However, the full treatment of their frequency and momentum dependence severely restricts numerical calculations. A significant advancement requires an efficient treatment of the high-frequency asymptotic behavior of the vertex functions. In this work, we first provide a detailed diagrammatic analysis of the high-frequency structures and their physical interpretation. Based on these insights, we propose a parametrization scheme, which captures the whole high-frequency domain for arbitrary values of the Coulomb interaction and electronic density, and we discuss the details of its algorithmic implementation in many-body solvers based on parquet-equations as well as functional renormalization group schemes. Finally, we assess its validity by comparing our results for a single impurity Anderson model with exact diagonalization calculations. The proposed parametrization is pivotal for the algorithmic development of all quantum many-body methods based on vertex functions arising from both local and non-local static microscopic interactions as well as effective dynamic interactions which uniformly approach a static value for large frequencies. In this way, our present technique can substantially improve vertex-based diagrammatic approaches including spatial correlations beyond dynamical mean-field theory.

H-COUP Version 2: A program for one-loop corrected Higgs boson decays in non-minimal Higgs sectors

We present the concept of H-COUP_ver 2, which evaluates the decay rates (including higher order corrections) for the Higgs boson with a mass of 125GeV in various extended Higgs models. In the previous version (H-COUP_1.0), only a full set of the Higgs boson vertices are evaluated at one-loop level in a gauge invariant manner in these models. H-COUP_ver 2 contains all the functions of H-COUP_1.0. After shortly introducing these extended Higgs models and discussing their theoretical and experimental constraints, we summarize formulae for the renormalized vertices and the decay rates. We then explain how to install and run H-COUP_ver 2 with some numerical examples. Program summaryProgram title: H-COUP Version 2CPC Library link to program files: http://dx.doi.org/10.17632/f88szmrj5x.2Developer’s repository link: http://www-het.phys.sci.osaka-u.ac.jp/ hcoup/Licensing provisions: GPLv3Programming language: Fortran90Journal Reference of previous version: Comput. Phys. Commun. 233 (2018), 134–144Does the new version supersede the previous version?: YesReasons for the new version: The previous version (H-COUP_1.0), which numerically evaluates the full set of one-loop corrected vertex functions for the Higgs boson with a mass of 125 GeV, does not automatically provide the decay rates, the total decay width and branching ratios. In addition, QCD corrections have not been included in the previous version.Summary of revisions: Decay branching ratios and the total decay width for the Higgs boson with NLO electroweak and NNLO QCD corrections are added as outputs.Nature of problem: Decay rates for the Higgs boson and the total decay width are numerically evaluated at NLO for electroweak and NNLO for QCD in the Higgs singlet model, four types (Type-I, Type-II, Type-X, Type-Y) of two Higgs doublet models with a softly-broken Z2 symmetry and the inert doublet model.Solution of method: Electroweak and QCD corrections to the decay rates are computed by the improved on-shell scheme and the MS¯ scheme, respectively.Additional comments including restrictions and unusual features: All functions of the previous version are included in H-COUP_ver 2.

Dynamically screened vertex correction to GW

Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\mathrm{\ensuremath{\Sigma}}$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the $GW$ approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction $W$) self-energy diagrams lead to improved electron spectral functions (SFs) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral functions. The resolution of this difficulty has been demonstrated in our previous works. The main idea is to represent the self-energy operator in a Fermi golden rule form which leads to a manifestly positive definite SF and allows for a very efficient numerical algorithm. So far, the method has only been applied to the three-dimensional electron gas, which is a paradigmatic system, but a rather simple one. Here we systematically extend the method to two dimensions including realistic systems such as monolayer and bilayer graphene. We focus on one of the most important vertex function effects involving the exchange of two particles in the final state. We demonstrate that it should be evaluated with the proper screening and discuss its influence on the quasiparticle properties.

Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation

We solve the anisotropic, full-bandwidth and non-adiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The non-adiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface restricted Eliashberg-theory calculations. We find that non-adiabatic contributions to the superconducting gap can be positive, negative or negligible, depending on the dimensionality of the considered system, the degree of non-adiabaticity, and the coupling strength. We further examine non-adiabatic effects on the transition temperature and the electron-phonon coupling constant. Our treatment emphasizes the importance of overcoming previously employed approximations in estimating the impact of vertex corrections on superconductivity and opens a pathway to systematically study vertex correction effects in systems such as high-$T_c$, flat band and low-carrier density superconductors.

Exact muffin-tin orbital based fully relativistic simulation of device materials: Electronic charge and spin current

We report the implementation of the fully relativistic exact muffin-tin orbital (EMTO) method for both first-principles electronic structure and quantum transport simulation of magnetic and nonmagnetic device materials. We consider a device-material system containing the inevitable atomic disorders in contact with different electrode materials. The Kohn-Sham Dirac equations for both cases with and without spin polarization are self-consistently solved for the central device-material system with the Green's function method. The fully relativistic charge-current density, conventional Pauli spin current density, and transmission coefficient are formulated with the nonequilibrium Green's function technique. To treat the influence of disordered defects/impurities, we combine the nonequilibrium Green's function in the Keldysh space with the coherent potential approximation, and account for the multiple disorder scattering by vertex corrections to a two-Green's-function correlator to calculate the disorder-averaged charge and spin current density. As a demonstration of the present implementation, we calculate the electronic structure of the bulk Pt, Co, and HgTe and Rashba-type surface states of Au and Ag/Ag2Bi1 alloy surfaces. We find that the EMTO electronic structures of all the calculated systems agree well with the results of the projector-augmented wave method. The electronic charge and spin transport implementations are tested with perfect and disordered Cu/Co/Pt/Cu junctions. The important effects of interface and atomic disorders are illustrated for the spin transport in the presence of relativistic effects. The implementation of the fully relativistic EMTO-based device-material simulation provides an important tool for analyzing both the charge and spin transport through nanostructures and materials, significantly extending the capability of first-principles material design for spintronic device applications.

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. The routinely used single-shot GW-approximation (G0W0) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth to check how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of non-interacting G such that only diagonal elements are retained, whereas, the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle bandgap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7% that validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms like the vertex correction.

Transverse Ward-Takahashi identities and full vertex functions in different representations of QED3 * * Supported in part by the National Natural Science Foundation of China (11475085, 11535005, 11690030), the National Major state Basic Research and Development (2016YFE0129300) and the Anhui Provincial Natural Science Foundation (1908085MA15)

We derive the transverse Ward-Takahashi identities (WTI) of N-dimensional quantum electrodynamics by means of the canonical quantization method and the path integration method, and subsequently attempt to prove that QED3 is solvable based on the transverse and longitudinal WTI, indicating that the full vector and tensor vertices functions can be expressed in terms of the fermion propagators in QED3. Further, we discuss the effect of different γ matrix representations on the full vertex function.

Band alignment at the CaF2/Si(111) interface through advanced electronic structure calculations

We determine the band alignment at the ${\mathrm{CaF}}_{2}/\mathrm{Si}(111)$ interface through various advanced electronic structure methods. This interface is experimentally well studied and serves as an ideal test case to examine the accuracy of theoretical schemes. We use both global and range-separated hybrid functionals as well as $GW$ calculations including self-consistency and vertex corrections. Our calculation procedure accounts for residual strain resulting from the small mismatch in the lateral lattice constants at the interface to minimize the systematic error in the comparison with experiment. Both the hybrid functional and the $GW$ schemes give band alignments in overall good agreement with the experimental characterization. However, the considered methods yield sizable variations in the calculated band offsets, which do not originate from incorrect evaluations of the band gaps but rather from different inherent relative positions of the band edges. The comparison with experiment reveals that the global hybrid functional and the quasiparticle self-consistent $GW$ with vertex corrections give the most accurate description of the band alignment. We then determine the variation of the band offsets as a function of the amount of excess fluorine at the interface and attribute the experimental spread in the measured offsets to uncontrolled fluorine contamination.

Anomalous Magnetic Moment of an Electron in a Static Magnetic Field in the Topologically Massive 2D Electrodynamics

An analytic equation for the anomalous magnetic moment of an electron in a static magnetic field in the topologically massive 2D electrodynamics is obtained in the single-loop approximation. The asymptotic expressions describing the dependence of the anomalous magnetic moment on the dimensionless Chern–Simons parameter and the dynamic field parameter are determined in the limiting case of a relatively weak magnetic field. The applicability conditions for the results of calculations of the anomalous electron magnetic moment based on the evaluation of the vertex function in the 2D electrodynamics with the Chern–Simons term are established.