Application of the renormalization group technique to the problem of phase transition in one-dimensional metallic systems. I. Invariant couplings, vertex, and one-particle Green's function

1973 ◽  
Vol 12 (5-6) ◽  
pp. 529-545 ◽  
Author(s):  
N. Menyhard ◽  
J. S�lyom
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Green’S Function ◽  
Green's Function ◽  
One Dimensional ◽  
Group Technique ◽  
Metallic Systems

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Green’s function of a 2D Fermi system undergoing a topological phase transition

JETP Letters ◽  
1999 ◽  
Vol 69 (2) ◽  
pp. 141-147 ◽  
Author(s):  
V. P. Gusynin ◽  
V. M. Loktev ◽  
S. G. Sharapov
Keyword(s):  
Phase Transition ◽  
Green’S Function ◽  
Green's Function ◽  
Fermi System ◽  
Topological Phase ◽  
Topological Phase Transition
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