We map the ground-state phase diagram of the quarter-filled spinless Su-Schrieffer-Heeger chain with nearest-neighbor interactions by combining exact diagonalization (ED) and density-matrix renormalization group (DMRG) under twist-averaged boundary conditions to suppress shell effects. A unified scaling analysis of the equal-time charge structure factor $S_{\mathrm{cdw}}\left(q\right)$—including the size dependence of $S_{\mathrm{cdw}}\left(q_{min}\right)$, the extrapolation of $S_{\mathrm{cdw}}\left(q_{min}\right)/L$ versus $1/L$, the evolution of $K_{\mathrm{eff}}\left(L\right)=\frac{1}{2}L{S}_{\mathrm{cdw}}\left(q_{min}\right)$, and the power-law behavior of $S_{\mathrm{cdw}}\left(2k_F\right)$—disentangles phase separation (PS), Luttinger liquids with pairing-dominated correlations ($K>1/2$), Luttinger liquids dominated by $2k_F$ bond-order-wave (BOW) correlations ($K<1/2$), and a long-range $2k_F$ charge-density-wave (CDW) phase. The phase structure, controlled by the interaction $V/t$ and dimerization $\delta t/t$, is as follows: PS for $V/t\lesssim -2$; a pairing-dominated Luttinger liquid for $-2<V/t<0$; for $V/t>0$ and moderate $|\delta t/t|$ the system realizes a $2k_F$-BOW-dominated Luttinger liquid; and for approximately $V/t\gtrsim 1.5$ together with $|\delta t/t|\lesssim 0.9$ it enters a long-range $2k_F$ CDW, whose domain expands toward smaller $|\delta t/t|$ with increasing $V/t$. Quantitative agreement between ED and DMRG across system sizes and boundary treatments underscores the robustness of this phase map and provides a benchmark for the competition between interactions and dimerization in one-dimensional dimerized chains.

Close

PrevNext

View figure in article

• Charge density waves
• Order parameters
• Phase diagrams
• 1-dimensional systems
• Strongly correlated systems
• Exact solutions for many-body systems
• Mean field theory
• Su-Schrieffer-Heeger model