Functional Renormalization Group Analysis of the Half-Filled One-Dimensional Extended Hubbard Model

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, also known as a “bond order wave” 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.

Figure 1

Discretization of the momenta in the Brillouin zone. This figure shows the case $N=10$.

Figure 2

The flows of SDW (solid lines), CDW (dotted lines), BSDW (dashed lines), BCDW (dotted-dashed lines) susceptibilities as function of $\ell$ for $U=1$, and $V=0.46$, 0.54, 0.62. The left column is for $N=2$, corresponding to standard $g$-ology, and the right column is for $N=50$.

Figure 3

The shifts of the SDW-BCDW and BCDW-CDW phase boundaries with the number of momentum divisions $N$.

Figure 4

The phase diagram of one-dimensional EHM at half-filling in the weak-coupling regime.