Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface

Abstract

We calculate zero-temperature correlation functions for a model of 2D interacting electrons with short-range interactions and a square Fermi surface. The model was arrived at by mapping electronic states near a square Fermi surface with Hubbard-like interactions onto one-dimensional quantum chains, retaining terms which can be written in terms of bosonic density operators. Interactions between orthogonal chains, corresponding to orthogonal faces of the square Fermi surface, are neglected. The correlation functions become sums of Luttinger-type correlation functions due to the bosonic model. However, the correlation function exponents differ in form from those of the Luttinger model. As a consequence, the simple scaling relations found to exist between the Luttinger model exponents, do not carry over to the leading exponents of our model. We find that for repulsive effective interactions, charge-density wave/spin-density wave instabilities are dominant. We do not consider d-wave instabilities here.

12 pages, no figures; to be published in Physical Review B

References in corpus (2)

• Classification and Stability of Phases of the Multicomponent One-Dimensional Electron Gas
• Does the Hubbard Model Show $d_{x^2-y^2}$ Superconductivity?

Cited by in corpus (12)

• Singular Fermi Liquids
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Field-theoretical renormalization group for a flat two-dimensional Fermi surface
• Correlation Energy of a Weakly Interacting Fermi Gas
• Ground state phase diagram of the repulsive fermionic $t-t^{\prime }$ Hubbard model on the square lattice from weak-coupling
• Self-energy corrections to anisotropic Fermi surfaces
• Adjacent face scattering of electrons on a square Fermi surface
• Luttinger liquid fixed point for a 2D flat Fermi surface
• Exact solution of a 2D interacting fermion model
• Fermions in two dimensions, bosonization, and exactly solvable models
• Gauge invariance, correlated fermions, and photon mass in 2+1 dimensions
• Deformation of anisotropic Fermi surfaces due to electron-electron interactions