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

TL;DR

This study maps the phase diagram of the one-dimensional half-filled extended Hubbard model using advanced numerical techniques, identifying the BOW phase and characterizing phase transitions with high accuracy across different interaction regimes.

Contribution

It provides a comprehensive and quantitatively validated phase diagram of the extended Hubbard model, including the BOW phase and transition types, using multiple physical quantities and cross-checks.

Findings

BOW phase exists between CDW and SDW phases

Transition from continuous to first order at tricritical point

BOW phase vanishes at the critical end point

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 $(U_{\rm t}, V_{\rm t}) \approx (5.89t, 3.10t)$ and the BOW phase vanishes at the critical end point $(U_{\rm c}, V_{\rm c}) \approx (9.25t, 4.76t)$.