Phase diagram of the one-dimensional half-filled extended Hubbard model

Abstract

We study the ground state of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction $U$ ($V$) and nearest-neighbor hopping $t$. In order to obtain an accurate phase diagram, we consider various physical quantities such as the charge gap, spin gap, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter using the density-matrix renormalization group technique. We confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to do a cross-check to demonstrate the validity of our estimations. Thus, our results agree quantitatively with the renormalization group results in the weak-coupling regime ($U\lesssim 2t$), with the perturbation results in the strong-coupling regime ($U\gtrsim 6t$), and with the quantum Monte Carlo results in the intermediate-coupling regime. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point $(U_{\mathrm{t}},V_{\mathrm{t}})\approx (5.89t,3.10t)$ and the BOW phase vanishes at the critical end point $(U_{\mathrm{c}},V_{\mathrm{c}})\approx (9.25t,4.76t)$.

arXiv comment4 pages, 5 figures

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