Vertex Corrections Research Articles

Pressure dependency of electron-phonon renormalization in diamond

Employing ab initio many-body perturbation theory, the carrier-phonon and carrier-carrier vertex functions are evaluated in diamond crystal under different hydrostatic pressure up to 140GPa and the phonon induced quasiparticle renormalization is measured at diverse linear and non-linear pressure regimes. Our results illustrate that the degree of carrier coupling to phonon satellite differs substantially from linear to non-linear regimes, due to changing the nature of the carrier dynamics. Particularly, reduction of the phonon induced renormalization with increasing pressure on the system is an indication of a transition from strong to a weak polaronic nature, which is in good accordance with experimental and theoretical studies. It demonstrates the significant role of the pressure in tuning the electron phonon coupling in a system. Furthermore, going to the higher pressure yields relevant discrepancy in electron energies from second-order phonon-induced to the first-order phonon perturbation. Our study recommends the hydrostatic pressure adjusts the significant contribution of electron-phonon self-energy in the electronic-related features of carbon-based materials as a new probe.

Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections

A few self-consistent schemes to solve the Hedin equations are presented. They include vertex corrections of different complexity. Commonly used quasiparticle approximation for the Green function and static approximation for the screened interaction are avoided altogether. Using alkali metals Na and K as well as semiconductor Si and wide gap insulator LiF as examples, it is shown that both the vertex corrections in the polarizability P and in the self energy $\Sigma$ are important. Particularly, vertex corrections in $\Sigma$ with proper treatment of frequency dependence of the screened interaction always reduce calculated band widths/gaps, improving the agreement with experiment. The complexity of the vertex included in P and in $\Sigma$ can be different. Whereas in the case of polarizability one generally has to solve the Bethe-Salpeter equation for the corresponding vertex function, it is enough (for the materials in this study) to include the vertex of the first order in the self energy. The calculations with appropriate vertices show remarkable improvement in the calculated band widths and band gaps as compared to the self-consistent GW approximation as well as to the self-consistent quasiparticle GW approximation.

Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections

In various multiorbital systems, the emergence of the orbital fluctuations and its role on the pairing mechanism attract increasing attention. To archive deep understanding on these issues, we perform the functional-renormalization-group (fRG) study for the two-orbital Hubbard model. The vertex corrections for the electron-boson coupling ($U$-VC), which are dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG equation. We reveal that the dressed electron-boson coupling for the charge-channel, $U_{eff}^c$, becomes much larger than the bare Coulomb interaction, $U^0$, due to the $U$-VC in the presence of moderate spin fluctuations. For this reason, the attractive pairing interaction due to the charge or orbital fluctuations is enlarged by the factor $(U_{eff}^c/U^0)^2 >> 1$. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel $U$-VC, because of the relation $U_{eff}^s << U^0$. The present study demonstrates that the orbital or charge fluctuation pairing mechanism can be realized in various multiorbital systems thanks to the $U$-VC, such as in Fe-based superconductors.

Functional flows in QED and the modified Ward–Takahashi identity

In the functional renormalisation group approach to gauge theory, the Ward–Takahashi identity is modified due to the presence of an infrared cutoff term. It take the most accessible form for the Wilsonian effective action. In the present work we solve these identities, partially, for the Wilsonian effective action of QED. In particular, we compute the longitudinal part of the photon two point vertex function as a momentum-dependent function in the presence of the cutoff k. The resultant Wilsonian effective action carries form factors that originate from the modified Ward–Takahashi identity. We show how this result carries over to the one-particle-irreducible effective action.

Dynamical gap generation in graphene with frequency-dependent renormalization effects

We study the frequency dependencies in the renormalization of the fermion Greens function for the $\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.

Analysis of the $B_{s}\rightarrow \bar{D}^{0} \phi$ decay

In this paper we analyzed the $ B_{s}\rightarrow \bar{D}^{0} \phi$ decay within different frameworks. At first we consider the naive factorization (NF) and the QCD factorization (QCDF) approach, where the final states are a pseudoscalar meson and vector meson; then we consider the final state interaction (FSI) effect, where the intermediate state is $ D_{s}^{\ast-}K^{+}$ to improve the branching ration. In QCDF we considered the nonfactorizable corrections, such as vertex correction and hard spectator interactions. First observation of the $ B_{s} \rightarrow \bar{D}^{0} \phi$ decay is reported using pp collision data, corresponding to an integrated luminosity of 1.0 fb-1, collected by the LHCb experiment at a center-of-mass energy of 7TeV. Our results in the naive factorization approach is $ 8.73^{+0.01}_{-0.01} \times 10^{-7}$ and in QCDF approach is $ 4.03^{+0.01}_{-0.02} \times 10^{-6}$ and the improved branching ratio is $ 1.84^{+0.18}_{-0.17} \times 10^{-5}$ , when we consider the final state interaction effect in energy scale $ \mu = m_{b}$ . It is near the experimental value, which is $ 2.3\times 10^{-5}$ .

Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization

We evaluate in the framework of QCD factorization the two-loop vertex corrections to the decays $\bar{B}_{(s)}\to D_{(s)}^{(\ast)+} \, L^-$ and $\Lambda_b \to \Lambda_c^+ \, L^-$, where $L$ is a light meson from the set $\{\pi,\rho,K^{(\ast)},a_1\}$. These decays are paradigms of the QCD factorization approach since only the colour-allowed tree amplitude contributes at leading power. Hence they are sensitive to the size of power corrections once their leading-power perturbative expansion is under control. Here we compute the two-loop ${\cal O}(\alpha_s^2)$ correction to the leading-power hard scattering kernels, and give the results for the convoluted kernels almost completely analytically. Our newly computed contribution amounts to a positive shift of the magnitude of the tree amplitude by $\sim 2$\%. We then perform an extensive phenomenological analysis to NNLO in QCD factorization, using the most recent values for non-perturbative input parameters. Given the fact that the NNLO perturbative correction and updated values for form factors increase the theory prediction for branching ratios, while experimental central values have at the same time decreased, we reanalyze the role and potential size of power corrections by means of appropriately chosen ratios of decay channels.

Spectral weight suppression in response functions of ultracold fermion-boson mixtures

We study the dynamical response of ultracold fermion-boson mixture in the Bogoliubov regime, where the interactions between fermionic impurities and bosonic excitations (phonons) are described by an effective Frohlich model under the Bogoliubov approximation. A characteristic suppression of the single-particle spectral weight is found in the small momentum region where the impurity band and phonon mode intersect. Using diagrammatic technique we compute the Bragg spectra as well as the momentum dependent force-force correlation function. We fnd that both of them are heavily affected by the spectral weight suppression effect at low impurity densities in both 1D and 2D systems. We show that the the spectral weight suppression feature in Bragg spectra, which was previously found in the quantum Monte Carlo simulations and which cannot be recovered by the random phase approximation, can be accurately reproduced with the help of vertex corrections.

Publisher's Note: Cluster dynamical mean field theory study of antiferromagnetic transition in the square-lattice Hubbard model: Optical conductivity and electronic structure [Phys. Rev. B94, 085110 (2016)

We numerically study optical conductivity $\sigma (\omega )$ near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections, and to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature- and $\omega$-dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\omega$-dependence, and sharpen the Drude peak and a high-$\omega$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\sigma (\omega )$ at $\omega$=0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\sigma (\omega )$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.

Theory of quantum transport in disordered systems driven by voltage pulse

Predicting time-dependent quantum transport in the transient regime is important for understanding the intrinsic dynamic response of a nanodevice and for predicting the limit of how such a device can switch on or off a current. Theoretically, this problem becomes quite difficult to solve when the nanodevice contains disorder because the calculated transient current must be averaged over many disorder configurations. In this work, we present a theoretical formalism to calculate the configuration averaged time-dependent current flowing through a phase coherent device containing disorder sites where the transient current is driven by sharply turning on and off the external bias voltage. Our theory is based on the Keldysh nonequilibrium Green's function (NEGF) formalism and is applicable in the far from equilibrium nonlinear response quantum transport regime. The effects of disorder scattering are dealt with by the coherent potential approximation (CPA) extended in the time domain. We show that after approximations such as CPA and vertex corrections for calculating the multiple impurity scattering in the transient regime, the derived NEGFs perfectly satisfy a Ward identity. The theory is quantitatively verified by comparing its predictions to the exact solution for a tight-binding model of a disordered two-probe transport junction.

Excitation spectra of aromatic molecules within a real-spaceGW-BSE formalism: Role of self-consistency and vertex corrections

We present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the $GW$ and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against ${G}_{0}{W}_{0}$ calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the $GW$ approximation that include a local density approximation (LDA)--derived vertex function (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$) and quasiparticle-self-consistent (QS) iterations. We find that ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. ${G}_{0}{W}_{0}$ and $\mathrm{QS}GW{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ are more accurate for IPs, while ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and $\mathrm{QS}GW$ are best for EAs. For optical excitations, we find that perturbative $GW$-BSE underestimates the singlet excitation energy, while self-consistent $GW$-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which ${G}_{0}{W}_{0}$ energies are used for occupied orbitals and ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.

Cluster dynamical mean field theory study of antiferromagnetic transition in the square-lattice Hubbard model: Optical conductivity and electronic structure

We numerically study optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ near the ``antiferromagnetic'' phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and $\ensuremath{\omega}$ dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\ensuremath{\omega}$ dependence, and sharpen the Drude peak and a high-$\ensuremath{\omega}$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\ensuremath{\sigma}(\ensuremath{\omega})$ at $\ensuremath{\omega}=0$ in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\ensuremath{\sigma}(\ensuremath{\omega})$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.

Complex-mass shell renormalization of the higher-derivative electrodynamics

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron--positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.

Spin Hall and spin Nernst effects in a two-dimensional electron gas with Rashba spin-orbit interaction: Temperature dependence

Using the Matsubara Green's function formalism we calculate the temperature dependence of spin Hall and spin Nernst conductivities of a two-dimensional electron gas with Rashba spin-orbit interaction in the linear response regime. In the case of the spin Nernst effect we also include the contribution from spin-resolved orbital magnetization, which assures correct behavior of the spin Nernst conductivity in the zero-temperature limit. Analytical formulas for the spin Hall and spin Nernst conductivities are derived in some specific situations. Using the Ioffe-Regel localization criterion, we have also estimated the range of parameters where the calculated results for the spin Hall and spin Nernst conductivities are applicable. Analytical results show that the vertex correction totally suppresses the spin Hall conductivity at arbitrary temperature. The spin Nernst conductivity, in turn, vanishes at $T=0$ when the orbital contribution is taken into account, but generally is nonzero at finite temperatures.

Generalized nonequilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method to do disorder average, the important effects of disorders remain largely un-explored or poorly understood. Here, we report a generalized non-equilibrium vertex correction method with coherent potential approximation for the non-equilibrium quantum transport simulation of disordered nanoelectronics. In this method, the disorder average of various Green's functions are computed by a generalized coherent potential approximation. A generalized non-equilibrium vertex correction algorithm is then developed to calculate disorder average of the product of any two real time single-particle Green's functions. We obtain nine non-equilibrium vertex corrections and find they can be solved by a set of simple linear equations. As a result, the averaged non-equilibrium density matrix and various important transport properties, including averaged current, disordered induced current fluctuation and the averaged shot noise, can all be efficiently computed in a unified simple scheme. Moreover, the relationship between the non-equilibrium vertex correction method and the non-equilibrium coherent potential approximation theory is clarified, and we prove the non-equilibrium coherent potential equals the non-equilibrium vertex correction and this equivalence is guaranteed by the Keldysh's formulas. In addition, a generalized form of conditionally averaged non-equilibrium Green's function is derived to incorporate with density functional theory to enable first-principles quantum transport simulation. Our approach provides a unified, efficient and self-consistent method for simulating non-equilibrium quantum transport through disordered nanoelectronics.

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases

Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly inter- acting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong coupling theories rely heavily on the so-called many-body T-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) becomes smaller above three dimensions, we propose an alternative way to reorganize Feynman diagrams and develop a theoretical framework for interacting Fermi gases beyond the ladder approximation. As an application, we solve the equation of state for three- and two-dimensional strongly interacting fermions and find excellent agreement with experimental [Science 335, 563 (2012)] and other theoretical results above the temperature 0.5TF .

Microscopic theory on charge transports of a correlated multiorbital system

Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, $\rho_{ab}$, and the Hall coefficient in the weak-field limit, $R_{\textrm{H}}$, in addition to the magnetic properties and the electronic structure, for a $t_{2g}$-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy ($\Sigma$), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the Aslamasov-Larkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the $\Sigma$ CVC and the MT CVC. Second, $\rho_{ab}$ and $R_{\textrm{H}}$ near the AF QCP have high-temperature region, governed mainly by the $\Sigma$ CVC, and low-temperature region, governed mainly by the $\Sigma$ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only $R_{\textrm{H}}$ at low temperatures, although $R_{\textrm{H}}$ at high temperatures and $\rho_{ab}$ at all temperatures considered are sufficiently described by including only the $\Sigma$ CVC. I also achieved the qualitative agreement with several experiments of Sr$_{2}$RuO$_{4}$ or Sr$_{2}$Ru$_{0.975}$Ti$_{0.025}$O$_{4}$. Moreover, I showed several better points of this theory than other theories.

W∞algebras, Hawking radiation, and information retention by stringy black holes

We have argued previously, based on the analysis of two-dimensional stringy black holes, that information in stringy versions of four-dimensional Schwarzschild black holes (whose singular regions are represented by appropriate Wess-Zumino-Witten models) is retained by quantum $W$-symmetries when the horizon area is not preserved due to Hawking radiation. It is key that the exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole requires a contribution from $W_\infty$ generators in its vertex function. The latter correspond to delocalised, non-propagating, string excitations that guarantee the transfer of information between the string black hole and external particles. When infalling matter crosses the horizon, these topological states are excited via a process: (Stringy black hole) + infalling matter $\rightarrow $ (Stringy black hole)$^\star$, where the black hole is viewed as a stringy state with a specific configuration of $W_\infty$ charges that are conserved. Hawking radiation is then the reverse process, with conservation of the $W_\infty$ charges retaining information. The Hawking radiation spectrum near the horizon of a Schwarzschild or Kerr black hole is specified by matrix elements of higher-order currents that form a phase-space $W_{1+\infty}$ algebra. We show that an appropriate gauging of this algebra preserves the horizon two-dimensional area classically, as expected because the latter is a conserved Noether charge.

Conserving approximations for response functions of the Fermi gas in a random potential

We scrutinize the diagrammatic perturbation theory of noninteracting electrons in a random potential with the aim to accomplish a consistent comprehensive theory of quantum diffusion. Ward identity between the one-electron self-energy and the two-particle irreducible vertex is generally not guaranteed in the perturbation theory with only elastic scatterings. We show how the Ward identity can be established in practical approximations and how the functions from the perturbation expansion should be used to obtain a fully consistent conserving theory. We derive the low-energy asymptotics of the conserving full two-particle vertex from which we find an exact representation of the diffusion pole and of the static diffusion constant in terms of Green functions of the perturbation expansion. We illustrate the construction on the leading vertex corrections to the mean-field diffusion due to maximally-crossed diagrams responsible for weak localization.

Emergent geometry from field theory: Wilson’s renormalization group revisited

We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture. We claim that the AdS$_{3}$/CFT$_{2}$ duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large$-N_{s}$ limit, where $N_{s}$ is the number of fermion flavors.