Vertex Function, Coupling Constant, and Composite Particle

1962 ◽  
Vol 125 (2) ◽  
pp. 761-770 ◽  
Author(s):  
Lu Sun Liu
Keyword(s):  
Vertex Function ◽  
Composite Particle ◽  
Coupling Constant

Vertex function and composite particle

1967 ◽  
Vol 47 (3) ◽  
pp. 400-409 ◽  
Author(s):  
E. Tirapegui
Keyword(s):  
Vertex Function ◽  
Composite Particle

VERTEX FUNCTION OF A STRONGLY INTERACTING ELECTRON-HOLE PAIR NEAR THE FERMI SURFACE

1995 ◽  
Vol 09 (17) ◽  
pp. 1097-1105
Author(s):  
S.L. GARAVELLI ◽  
A. FERRAZ ◽  
J.A. HENDERSON ◽  
Y. OHMURA
Keyword(s):  
Fermi Surface ◽  
Vertex Function ◽  
Infinite Order ◽  
Energy Scale ◽  
Coupling Constant ◽  
Interacting Particles ◽  
Third Order ◽  
Electron Hole ◽  
Strongly Interacting ◽  
Electron Hole Pair

In this work we calculate and compare all the second- and third-order diagrams of the irreducible part K of the electron-hole scattering function for strongly interacting particles near the Fermi surface. We show that the exchange ladder diagrams for K are indeed the most singular diagrams up to this order of perturbation theory in the proximity of the Fermi surface. From this result emerges a new low energy scale parameter and a new effective coupling constant associated with the strongly interacting regime. The summation of exchange ladder diagrams to infinite order produces a purely imaginary pole in K. As a result the vertex function Γ diverges and the Fermi liquid becomes unstable in this strongly interacting regime.

scholarly journals Composite Particle and Vertex Function in the Nonrelativistic Off-Shell Theory

1967 ◽  
Vol 37 (5) ◽  
pp. 1003-1028 ◽  
Author(s):  
Nobuhiko Mishima ◽  
Miwae Yamazaki
Keyword(s):  
Vertex Function ◽  
Shell Theory ◽  
Composite Particle

RECOVERY OF GAUGE INVARIANCE IN STRONG-COUPLING QED

1992 ◽  
Vol 07 (29) ◽  
pp. 7239-7262 ◽  
Author(s):  
KONDO KEI-ICHI
Keyword(s):  
Critical Point ◽  
Vertex Function ◽  
Mean Field ◽  
Mass Function ◽  
Dyson Equation ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Massive Solution ◽  
Bare Coupling Constant ◽  
Arbitrary Gauge

Under a novel ansatz for the vertex function, the Schwinger- Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff Λ, there exists a bifurcation point ec(Λ) of the bare coupling constant above which the trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects the Ward-Takahashi identity, the critical point ec(∞) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky’s scaling of the essential-singularity type and that the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.

scholarly journals Composite Particle and Vertex Function in the Nonrelativistic Off-Shell Theory

1967 ◽  
Vol 38 (5) ◽  
pp. 1205b-1205b
Author(s):  
Nobuhiko Mishima ◽  
Miwae Yamazaki
Keyword(s):  
Vertex Function ◽  
Shell Theory ◽  
Composite Particle

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model to Improve Density Function Calculations

2019 ◽  
Author(s):  
Xianghai Sheng ◽  
Lee Thompson ◽  
Hrant Hratchian
Keyword(s):  
Density Functional Theory ◽  
Exchange Coupling ◽  
Density Functional ◽  
Spin Crossover ◽  
Coupling Constants ◽  
Spin Projection ◽  
Coupling Constant ◽  
Projection Model ◽  
Functional Theory

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the Approximate Projection model. Results show that improvements using the Approximate Projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin-projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin-projection can be important for both geometry optimization and energy evaluations. The Approximate Project model provides an affordable and practical approach for effectively correcting spin-contamination errors in molecular exchange coupling constant and spin crossover gap calculations.

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