Two-loop renormalization group calculation of response functions for a two-dimensional flat Fermi surface

2008 ◽  
Vol 78 (19) ◽  
Author(s):  
Eberth Correa ◽  
Hermann Freire ◽  
Alvaro Ferraz
Keyword(s):  
Renormalization Group ◽  
Fermi Surface ◽  
Two Dimensional ◽  
Response Functions ◽  
Renormalization Group Calculation

RENORMALIZATION GROUP OF A TWO-DIMENSIONAL PATCHED FERMI SURFACE

2003 ◽  
Vol 17 (04) ◽  
pp. 167-174 ◽  
Author(s):  
A. FERRAZ
Keyword(s):  
Renormalization Group ◽  
Continuous Function ◽  
Fermi Surface ◽  
Fermi Liquid ◽  
Anomalous Dimension ◽  
Luttinger Liquid ◽  
Two Dimensional ◽  
Infinite Slope ◽  
Fermi Liquid Theory ◽  
Liquid Theory

Using the renormalization group we calculate the single particle Green's function G and the momentum occupation function [Formula: see text] for a quasiparticle in a two-dimensional Fermi Surface (FS) composed of four symmetric patches with both flat and curved arcs in [Formula: see text]-space. We show that G develops an anomalous dimension as a result of the vanishing of the quasiparticle weight at the FS. [Formula: see text] is a continuous function of [Formula: see text] with an infinite slope at FS for CU*2/(1 - CU*2) < 1. This result resembles a Luttinger liquid and indicates the breakdown of Fermi liquid theory in this regime.

AN EXACT FINITE FIELD RENORMALIZATION GROUP CALCULATION ON A TWO-DIMENSIONAL FRACTAL LATTICE

2000 ◽  
Vol 11 (02) ◽  
pp. 257-275 ◽  
Author(s):  
J. F. NYSTROM
Keyword(s):  
Renormalization Group ◽  
Finite Field ◽  
Spin System ◽  
Spin Coupling ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Free Energy Surface ◽  
Fractal Lattice ◽  
Real Space Renormalization Group ◽  
Renormalization Group Calculation

A two-dimensional fractal lattice, herein referred to as the tetrahedral gasket, is used as a model for an exact two-dimensional real-space renormalization group calculation. It is shown that this Ising spin-system has exact solutions which includes a nontrivial phase transition even in the presence of a finite field. The calculation also introduces a new analysis tool, the free energy surface plot, which gives further insight into the phase diagram of the spin-system. The discussion includes comments concerning the apparent preference of the system to maintain some finite entropy, even in the presence of an extremely large spin–spin coupling.

scholarly journals Renormalization group for two-dimensional fermions with a flat Fermi surface

2002 ◽  
Vol 65 (9) ◽  
Author(s):  
Sébastien Dusuel ◽  
Fernao Vistulo de Abreu ◽  
Benoît Douçot
Keyword(s):  
Renormalization Group ◽  
Fermi Surface ◽  
Two Dimensional

scholarly journals Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Agnese Tagliavini ◽  
Cornelia Hille ◽  
Fabian Kugler ◽  
Sabine Andergassen ◽  
Alessandro Toschi ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Two Dimensional ◽  
Response Functions ◽  
Functional Renormalization Group ◽  
Self Energy ◽  
Numerical Effort ◽  
Physical Response ◽  
The Common ◽  
Made In

We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, performed with an algorithmic implementation which lifts some of the common approximations made in fRG calculations. In particular, in our fRG flow; (i) we take explicitly into account the momentum and the frequency dependence of the vertex functions; (ii) we include the feedback effect of the self-energy; (iii) we implement the recently introduced multiloop extension which allows us to sum up all the diagrams of the parquet approximation with their exact weight. Due to its iterative structure based on successive one-loop computations, the loop convergence of the fRG results can be obtained with an affordable numerical effort. In particular, focusing on the analysis of the physical response functions, we show that the results become independent from the chosen cutoff scheme and from the way the fRG susceptibilities are computed, i.e., either through flowing couplings to external fields, or through a “post-processing” contraction of the interaction vertex at the end of the flow. The presented substantial refinement of fRG-based computation schemes paves a promising route towards future quantitative fRG analyses of more challenging systems and/or parameter regimes.

scholarly journals TWO-LOOP RENORMALIZATION OF THE QUASIPARTICLE WEIGHT IN TWO-DIMENSIONAL ELECTRON SYSTEMS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1381-1384 ◽  
Author(s):  
JUN-ICHIRO KISHINE ◽  
NOBUO FURUKAWA ◽  
KENJI YONEMITSU
Keyword(s):  
Renormalization Group ◽  
Fermi Surface ◽  
Model Systems ◽  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Energy Process ◽  
Self Energy ◽  
Two Dimensional Electron Systems

We apply the renormalization-group (RG) approach to two model systems where the two-dimensional Fermi surface has portions which give rise to the logarithmically singular two-loop self-energy process.

Sign in / Sign up

Export Citation Format

Share Document