Vertex Corrections Research Articles

Role of Disorder in the Intrinsic Orbital Hall Effect.

The orbital Hall effect (OHE) has garnered much attention as a promising approach to realize highly efficient "orbitronic" devices with a wide range of materials. However, the existing theories that attempt to explain the experimental evidence focus on the intrinsic effect, neglecting the omnipresent disorder. Here, we formulate the impact of random defect scattering on the orbital Hall effect by a quantum Boltzmann equation and solve it for a generic two-band model including the in-scattering collision integral (vertex correction). In contrast to the common belief that the intrinsic OHE is robust against the disorder, we find that diffuse scattering by an arbitrarily weak disorder affects and can even fully suppress the intrinsic orbital Hall current, depending on the character of orbital states and the disorder.

All-electron first-principles GWΓ simulations for accurately predicting core-electron binding energies considering first-order three-point vertex corrections.

In the conventional GW method, the three-point vertex function (Γ) is approximated to unity (Γ ∼ 1). Here, we developed an all-electron first-principles GWΓ method beyond a conventional GW method by considering a first-order three-point vertex function (Γ(1) = 1 + iGGW) in a one-electron self-energy operator. We applied the GWΓ method to simulate the binding energies (BEs) of B1s, C1s, N1s, O1s, and F1s for 19 small-sized molecules. Contrary to the one-shot GW method [or G0W0(LDA)], which underestimates the experimentally determined absolute BEs by about 3.7eV for B1s, 5.1eV for C1s, 6.9eV for N1s, 7.8eV for O1s, and 5.8eV for F1s, the GWΓ method successfully reduces these errors by approximately 1-2eV for all the elements studied here. Notably, the first-order three-point vertex corrections are more significant for heavier elements, following the order of F > O > N > C > B1s. Finally, the computational cost analysis revealed that one term in the GWΓ one-electron self-energy operator, despite being computationally intensive, contributes negligibly (<0.1eV) to the C1s, N1s, O1s, and F1s.

Molecular Pairing in Twisted Bilayer Graphene Superconductivity.

We propose a theory for how the weak phonon-mediated interaction (J_{A}=1-4 meV) wins over the prohibitive Coulomb repulsion (U=30-60 meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A_{3}C_{60} family of molecular superconductors: Each AA stacking region of MATBG resembles a C_{60} molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced J_{A} has the form of an intervalley anti-Hund's coupling and is less suppressed than U by the Kondo screening near a Mott insulator. Additionally, we also considered an intraorbital Hund's coupling J_{H} that originates from the on-site repulsion of a carbon atom. Under a reasonable approximation of the realistic model, we prove that the renormalized local interaction between quasiparticles has a pairing (negative) channel in a doped correlated insulator at ν=±(2+δν), albeit the bare interaction is positive definite. The proof is nonperturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal U for superconductivity is predicted. In a large area of the parameter space of J_{A}, J_{H}, the ground state is found to have a nematic d-wave singlet pairing, which, however, can lead to a p-wave-like nodal structure due to the Berry's phase on Fermi surfaces (or Euler obstruction).

Electric conductivity of hot and dense nuclear matter

Transport coefficients play an important role in characterising hot and dense nuclear matter, such as that created in ultra-relativistic heavy-ion collisions (URHIC). In the present work we calculate the electric conductivity of hot and dense hadronic matter by extracting it from the electromagnetic spectral function, through its zero energy limit at vanishing 3-momentum. We utilise the vector dominance model (VDM), in which the photon couples to hadronic currents predominantly through the ρ meson. Therefore, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot and dense hadronic matter, by dressing its pion cloud with π-ρ, π-σ, π-K, N-hole, and Δ-hole loops. We then introduce vertex corrections to maintain gauge invariance. Finally, we analyze the low-energy transport peak as a function of temperature and baryon chemical potential, and extract the conductivity along a proposed phase transition line.

One-loop QCD amplitudes in the Feynman-diagram gauge

Scattering amplitudes for the massless QCD process, qq¯→q′q¯′, are calculated in the one-loop order in the Feynman-Diagram (FD) gauge, where gluons are quantized on the light cone with opposite direction of the three-momenta. We find non-decoupling of the Faddeev-Popov ghosts and nonconventional UV singularities in dimensional regularization. The known QCD amplitudes with asymptotic freedom are reproduced only after summing propagator and vertex corrections. By quantizing gluons in the Feynman gauge on the FD gauge background, we obtain the one-loop improved FD gauge amplitudes. Published by the American Physical Society 2024

Vertex corrections on the conductivity of high-Tc superconductors in the spin polaron formulation

Vertex corrections on the conductivity of high-Tc superconductors in the spin polaron formulation

Ward identity preserving approach for investigation of phonon spectrum with self-energy and vertex corrections

Ward identity preserving approach for investigation of phonon spectrum with self-energy and vertex corrections

Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

Loop correction and resummation of vertex functions for a self interacting scalar field in the de Sitter spacetime

We consider a massless and minimally coupled self interacting quantum scalar field theory in the inflationary de Sitter background of dimension four. The self interaction potential is taken to be either quartic, λϕ4/4!, or quartic plus cubic, λϕ4/4!+βϕ3/3! (λ>0). We compute the four and three point vertex functions up to two loop. The purely local or partly local part of these renormalised loop corrected vertex functions grow unboundedly after sufficient number of de Sitter e-foldings, due to the appearances of secular logarithms. We focus on the purely local part of the vertex functions and attempt a resummation of them in terms of the dynamically generated mass of the scalar field at late times. Such local logarithms have sub-leading powers compared to the non-local leading ones which can be resummed via the stochastic formalism. The variation of these vertex functions are investigated with respect to the tree level couplings numerically. Since neither the secular effect, nor the dynamical generation of field mass is possible in the Minkowski spacetime, the above phenomenon has no flat spacetime analogue. We have also compared our result with the ones that could be found via the recently proposed renormalisation group techniques. All these results suggest that at late times the value of the non-perturbative vertex function should be less than the tree level coupling.

Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1) -dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.

Reply to “Comment on ‘Towards exact solutions for the superconducting Tc induced by electron-phonon interaction' ”

In a series of papers, we have proposed a nonperturbative field-theoretic approach to deal with strong electron-phonon and strong Coulomb interactions. The key ingredient of such an approach is to determine the full fermion-boson vertex corrections by solving a number of self-consistent Ward-Takahashi identities. Palle argued that our Ward-Takahashi identities failed to include some important additional terms and thus are incorrect. We agree that our Ward-Takahashi identities have ignored some potentially important contributions and here give some remarks on the role played by the additional terms. Published by the American Physical Society 2024

Spin-dependent interactions in orbital-density-dependent functionals: Noncollinear Koopmans spectral functionals

The presence of spin-orbit coupling or noncollinear magnetic spin states can have dramatic effects on the ground-state and spectral properties of materials, in particular on the band structure. Here, we develop noncollinear Koopmans-compliant functionals based on Wannier functions and density-functional perturbation theory, targeting accurate spectral properties in the quasiparticle approximation. Our noncollinear Koopmans-compliant theory involves functionals of four-component orbital densities that can be obtained from the charge and spin-vector densities of Wannier functions. We validate our approach on four emblematic nonmagnetic and magnetic semiconductors where the effect of spin-orbit coupling goes from small to very large: the III-IV semiconductor GaAs, the transition-metal dichalcogenide WSe2, the cubic perovskite CsPbBr3, and the ferromagnetic semiconductor CrI3. The predicted band gaps are comparable in accuracy to state-of-the-art many-body perturbation theory and include spin-dependent interactions and screening effects that are missing in standard diagrammatic approaches based on the random phase approximation. While the inclusion of orbital- and spin-dependent interactions in many-body perturbation theory requires self-screening or vertex corrections, they emerge naturally in the Koopmans-functionals framework. Published by the American Physical Society 2024

Doping dependence and multichannel mediators of superconductivity: calculations for a cuprate model

We study two aspects of the superconductivity in a cuprate model system, its doping dependence and the influence of competing pairing mediators. We first include electron–phonon interactions beyond Migdal’s approximation and solve self-consistently, as a function of doping and for an isotropic electron–phonon coupling, the full-bandwidth, anisotropic vertex-corrected Eliashberg equations under a non-interacting state approximation for the vertex correction. Our results show that such pairing interaction supports the experimentally observed dx2−y2 -wave symmetry of the superconducting gap, but only in a narrow doping interval of the hole-doped system. Depending on the coupling strength, we obtain realistic values for the gap magnitude and superconducting critical temperature Tc close to optimal doping, rendering the electron–phonon mechanism an important candidate for mediating superconductivity in this model system. Second, for a doping near optimal hole doping, we study multichannel superconductivity, by including both vertex-corrected electron–phonon interaction and spin and charge fluctuations as pairing mechanisms. We find that both mechanisms cooperate to support an unconventional d-wave symmetry of the order parameter, yet the electron–phonon interaction is mainly responsible for the Cooper pairing and high critical temperature Tc . Spin fluctuations are found to have a suppressing effect on the gap magnitude and critical temperature due to their repulsive interaction at small coupling wave vectors.

Magnetic corrections to the QCD coupling: Strong field approximation

We compute the one-loop vertex function of the QCD coupling in the presence of an ultraintense magnetic field. From the vertex function, we extract the effective coupling and show that it grows with increasing magnetic field. We consider the quark-gluon vertex and the three-gluon vertex, accounting for the propagators of charged particles within the loops using the lowest Landau level approximation in order to satisfy the condition where the magnetic field is the largest energy scale. Under this approximation, we find that the contribution from the three-gluon vertex vanishes. Therefore, this result arises from the competition between the color charge associated to gluons and to quarks as well, with the former being larger than the latter. The behavior of the QCD coupling as a function of the magnetic field strength is analogous to that exhibited by the light-quark condensate, indicating the magnetic catalysis occurs. This increasing behavior stems from the dominant contribution of color charge associated to gluons in the vertex function. Published by the American Physical Society 2024

Polarized and unpolarized off-shell decay above the threshold* *Supported by UNAM Posdoctoral Program (POSDOC), and the Sistema Nacional de Investigadores (Mexico)

An analysis of the off-shell decay width is presented for both unpolarized and polarized gauge bosons in the scenario with the most general vertex function, which is expressed in terms of two -even ( and ) and one -odd ( ) anomalous couplings. The SM contributions to the coupling up to the one-loop level are also included. Explicit analytic results for the unpolarized and polarized square amplitudes and the four-body phase space are presented, out of which several observable quantities can be obtained straightforwardly. Regarding numerical analysis, a cross-check was performed via , where our model was implemented with the aid of FeynRules. We then considered the most stringent bounds on anomalous complex couplings and analyzed the effects of the polarizations of the gauge bosons through the polarized decay width as well as left-right and forward-backward asymmetries, which were found to be sensitive to new-physics effects. Particular focus was put on the effects of the absorptive parts of the anomalous couplings, which have been largely overlooked up to now in LHC analyses. It was found that the studied observable quantities, particularly the left-right asymmetries, can be helpful to search for effects of -violation in the coupling and set bounds on the absorptive parts. For completeness, we also analyzed the case of unpolarized gauge bosons.

Vertex corrections to conductivity in the Holstein model: A numerical-analytical study

Vertex corrections to conductivity in the Holstein model: A numerical-analytical study

Spin Hall effect: Symmetry breaking, twisting, and giant disorder renormalization

Atomically thin materials based on transition-metal dichalcogenides and graphene offer a promising avenue for unlocking the mechanisms underlying the spin Hall effect (SHE) in heterointerfaces. Here we develop a microscopic theory of the SHE for twisted van der Waals heterostructures that fully incorporates twisting and disorder effects and illustrate the critical role of symmetry breaking in the generation of spin Hall currents. We find that an accurate treatment of vertex corrections leads to a qualitatively and quantitatively different SHE than that obtained from the popular iη and ladder approximations. A pronounced oscillatory behavior of skew-scattering processes with twist angle θ is predicted, reflecting a nontrivial interplay of Rashba and valley-Zeeman effects and yields a vanishing SHE for θ=30∘ and, for graphene-WSe2 heterostructures, an optimal SHE for θ≈17∘. Our findings reveal disorder and broken symmetries as important knobs to optimize interfacial SHEs. Published by the American Physical Society 2024

Ghost-gluon vertex in the presence of the Gribov horizon: General kinematics

Correlation functions are important probes for the behavior of quantum field theories. Already at tree-level, the refined Gribov-Zwanziger (RGZ) effective action for Yang-Mills theories provides a good approximation for the gluon propagator, as compared to that calculated by nonperturbative methods such as lattice field theory and Dyson-Schwinger equations. However, the study of higher correlation functions of the RGZ theory is still at its beginning. In this work we evaluate the ghost-gluon vertex function in Landau gauge at one-loop level, in d=4 space-time dimensions for the gauge groups SU(2) and SU(3). More precisely, we extend the analysis conducted in [1] for the soft-gluon limit to an arbitrary kinematic configuration. We introduce renormalization group effects by means of a toy model for the running coupling and investigate the impact of such a model in the ultraviolet tails of our results. We find that RGZ results match fairly closely those from lattice simulations, Schwinger-Dyson equations and the Curci-Ferrari model for three different kinematic configurations. This is compatible with RGZ being a feasible theory for the strong interaction in the infrared regime. Published by the American Physical Society 2024

Converging many-body perturbation theory for ab-initio nuclear structure: Brillouin-Wigner perturbation series for closed-shell nuclei

Convergence aspects of nuclear many-body perturbation theory for ground states of closed-shell nuclei are explored using a Brillouin-Wigner formulation with a new vertex function enabling high-order calculations. A general formalism for Hamiltonian partitioning and a convergence criterion for the perturbation series are proposed. Analytical derivations show that with optimal partitioning, the convergence criterion for ground states can always be satisfied. This feature attributes to the variational principle and does not depend on the choice of an internucleon interaction or a many-body basis. Numerical calculations of the ground state energies of He4 and O16 with Daejeon16 and a bare N3LO potential in both harmonic-oscillator and Hartree-Fock bases confirm this finding.

Going Beyond the GW Approximation Using the Time-Dependent Hartree-Fock Vertex.

The time-dependent Hartree-Fock (TDHF) vertex of many-body perturbation theory (MBPT) makes it possible to extend TDHF theory to charged excitations. Here we assess its performance by applying it to spherical atoms in their neutral electronic configuration. On a theoretical level, we recast the TDHF vertex as a reducible vertex, highlighting the emergence of a self-energy expansion purely in orders of the bare Coulomb interaction; then, on a numerical level, we present results for polarizabilities, ionization energies (IEs), and photoemission satellites. We confirm the superiority of THDF over simpler methods such as the random phase approximation for the prediction of atomic polarizabilities. We then find that the TDHF vertex reliably provides better IEs than GW and low-order self-energies do in the light-atom, few-electron regime; its performance degrades in heavier, many-electron atoms instead, where an expansion in orders of an unscreened Coulomb interaction becomes less justified. New relevant features are introduced in the satellite spectrum by the TDHF vertex, but the experimental spectra are not fully reproduced due to a missing account of nonlinear effects connected to hole relaxation. We also explore various truncations of the self-energy given by the TDHF vertex, but do not find them to be more convenient than low-order approximations such as GW and second Born (2B), suggesting that vertex corrections should be carried out consistently both in the self-energy and in the polarizability.