Field Theory Renormalization Group: The Tomonaga-Luttinger Model Revisited

Abstract

We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We compute the anomalous dimension associated with the one-particle Green's functions $G_{(a)R}$. We calculate the RG equations for the renormalized forward couplings $g_{2R}$ and $g_{4R}$ up to two-loop order and demonstrate that they don't flow in the vicinities of the Fermi points (FPs). We solve the Callan-Symanzik equation for $G_{(a)R}$ in the neighborhood of the FPs. We calculate the related spectral function and the momentum distribution function at $p=k_F,p_0=\omega$. We compute the renormalized one-particle irreducible function ${\Gamma }_{(+)R}^{(2)}(p,p_0=0;\Lambda )$ and show it carries important spin-charge separation effects in agreement with well known results. Finally we discuss the implementation of the RG scheme taking into account the important simplifications produced by the Ward identities.

12 pages, 12 figures. Typos corrected and new references added

References in corpus (5)

• Temperature dependence of antiferromagnetic order in the Hubbard model
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Ward identities and Chiral anomaly in the Luttinger liquid
• Field-theoretical renormalization group for a flat two-dimensional Fermi surface
• Fermi Surface Renormalization in Two Spatial Dimensions

Cited by in corpus (2)

• Fermi surface renormalization and quantum confinement in the two-coupled chains model
• Confinement and quantum anomaly in quasi-1D spinless fermion chains