Exact electronic Green functions in a Luttinger liquid with long-range interactions

Abstract

We compute the 2-point (equal-time) electronic Green function in a Tomonaga-Luttinger system with long-range electron-electron interactions. We obtain an analytical expression for a "super long-range" potential of the form $V(x)=\frac{e^2{d}^{-\epsilon }}{|x{|}^{1-\epsilon }}$. As a consistency check of our computational technique we also consider the particular case of a Coulomb potential. Our result confirms the $\exp -C(logx{)}^{3/2}$ long-distance behavior first obtained by Schulz.

Latex, 11 pages, no figures. Version to appear in Phys. Rev. B. Added references, corrected sign and factor in equations (19) and (21)

References in corpus (3)

• Insulator-Metal Transition in One Dimension Induced by Long-Range Electronic Interactions
• Vacuum properties of a Non-Local Thirring-Like Model
• Non-local Thirring model at finite-temperature

Cited by in corpus (13)

• The Coulomb Luttinger liquid
• Interaction-range effects for fermions in one dimension
• Quantum quench dynamics of the Coulomb Luttinger model
• Conformal field theory in Tomonaga-Luttinger model with $1/r^{\beta }$ type long-range interactions
• Friedel oscillations in a Luttinger liquid with long-range interactions
• Ground states of long-range interacting fermions in one spatial dimension
• Tunneling conductance of long-range Coulomb interacting Luttinger liquid
• Effect of nonadiabatic switching of dynamic perturbations in 1d Fermi systems
• Correlations in interacting electron liquids: Many-body statistics and hyperuniformity
• Collective ground states in small lattices of coupled quantum dots
• Conformal properties of 1D quantum systems with long-range interactions
• Non local Thirring model with spin flipping interactions
• Nonmonotonic plasmon dispersion in strongly interacting Coulomb Luttinger liquids