Two-loop renormalization-group theory for the quasi-one-dimensional Hubbard model at half filling

TL;DR

This paper develops a two-loop renormalization-group theory for quasi-one-dimensional Hubbard models, analyzing excitation gaps and symmetry properties, with applications to ladder systems.

Contribution

It introduces a two-loop RG scheme with transverse momentum dependence for quasi-1D Hubbard models, extending previous 1D approaches and applying it to ladder systems.

Findings

Charge gap is suppressed but remains finite with interchain hopping.

Low-energy excitations exhibit SO(3) x SO(3) x U(1) symmetry when interchain hopping is large.

Method accurately estimates excitation gaps in ladder systems.

Abstract

We derive two-loop renormalization-group equations for the half-filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization-group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the g-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half-filled Hubbard model and obtain constraints on the g-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization-group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical bosonization and fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have SO(3) x SO(3) x U(1) symmetry when the interchain hopping exceeds the magnitude of the charge gap.