Functional Renormalization Group Analysis of the Half-filled One-dimensional Extended Hubbard Model

TL;DR

This paper employs a novel functional renormalization group approach to analyze the phase diagram of the half-filled one-dimensional extended Hubbard model, revealing a bond charge density wave phase and emphasizing the importance of irrelevant corrections.

Contribution

The study introduces a systematic FRG method that includes effects of scattering processes away from Fermi points, clarifying the phase diagram topology.

Findings

Confirmed existence of bond charge density wave near U=2V

Identified why earlier methods missed the BCDW phase

Showed irrelevant corrections can alter phase diagram topology

Abstract

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave (BCDW), also known as a ``bond order wave'' (BOW), near $U = 2V$ and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.