scholarly journals BOSONIZATION AND THE EIKONAL EXPANSION: SIMILARITIES AND DIFFERENCES

1996 ◽  
Vol 10 (17) ◽  
pp. 2111-2124 ◽  
Author(s):  
PETER KOPIETZ
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Background Field ◽  
Functional Integral ◽  
Integral Approach ◽  
Quasi Particle ◽  
Energy Behavior ◽  
Liquid Behavior ◽  
Correct Location ◽  
Eikonal Expansion

We compare two non-perturbative techniques for calculating the single-particle Green’s function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green’s function is first calculated for a fixed configuration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the quasi-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green’s function predicted by the eikonal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behavior of the spectral function, nor predicts the correct location of its singularities.

scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

scholarly journals HOW DOES A QUADRATIC TERM IN THE ENERGY DISPERSION MODIFY THE SINGLE-PARTICLE GREEN'S FUNCTION OF THE TOMONAGA–LUTTINGER MODEL?

2000 ◽  
Vol 14 (14) ◽  
pp. 1481-1499 ◽  
Author(s):  
TOM BUSCHE ◽  
PETER KOPIETZ
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Single Particle ◽  
Anomalous Dimension ◽  
Chemical Potential ◽  
Quadratic Term ◽  
Fermi Velocity ◽  
Energy Dispersion ◽  
Luttinger Model ◽  
Energy Behavior

We calculate the effect of a quadratic term in the energy dispersion on the low-energy behavior of the Green's function of the spinless Tomonaga–Luttinger model (TLM). Assuming that for small wave-vectors q= k-k F the fermionic excitation energy relative to the Fermi energy is v F q+q2/(2m), we explicitly calculate the single-particle Green's function for finite but small values of λ=q c /(2k F ). Here k F is the Fermi wave-vector, q c is the maximal momentum transfered by the interaction, and v F =k F /m is the Fermi velocity. Assuming equal forward scattering couplings g2=g4, we find that the dominant effect of the quadratic term in the energy dispersion is a renormalization of the anomalous dimension. In particular, at weak coupling the anomalous dimension is [Formula: see text], where γ is the anomalous dimension of the TLM. We also show how to treat the change of the chemical potential due to the interactions within the functional bosonization approach in arbitrary dimensions.

scholarly journals Collective Modes of an Ultracold6Li-40K Mixture in an Optical Lattice

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Z. G. Koinov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Optical Lattice ◽  
Random Phase ◽  
Fermi Gas ◽  
Functional Integral ◽  
Low Energy ◽  
Collective Modes ◽  
Legendre Transform ◽  
Goldstone Mode

A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green’s function and the Bethe-Salpeter equation for the two-particle Green’s function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to low-energy (Goldstone) mode, the two-species Fermi gas has a superfluid phase revealed by two roton-like minima in the asymmetric collective-mode energy.

scholarly journals Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum

2019 ◽  
Vol 15 (12) ◽  
pp. 6703-6711 ◽  
Author(s):  
Wenjie Dou ◽  
Tyler Y. Takeshita ◽  
Ming Chen ◽  
Roi Baer ◽  
Daniel Neuhauser ◽  
...  
Keyword(s):  
Green’S Function ◽  
Ionization Potential ◽  
Real Time ◽  
Green's Function ◽  
Second Order ◽  
Particle Spectrum ◽  
Quasi Particle
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