One-dimensional interacting Su-Schrieffer-Heeger model at quarter filling: An exact diagonalization study

This study explores the ground-state phase diagram and topological properties of the spinless 1D Su-Schrieffer-Heeger (SSH) model with nearest-neighbor (NN) interactions at quarter filling. We analyze key physical quantities such as the local electron density distribution, correlation functions for bond-order-wave (BOW) and charge-density-wave (CDW) -- by integrating twisted boundary conditions with the Lanczos technique and employing high-precision numerical diagonalization methods, complemented by a mean-field approximation (MFA) based on bond-order and charge-density modulation analysis. This approach enables precise identification of phase transition critical points. Our results indicate that the system exhibits a topologically trivial band insulating (BI) phase for strong attractive interactions, with its upper boundary forming a downward-opening curve peaking at $V/t\simeq-2.3$ and extending to $V/t\simeq-2.6$. Within $-2.6 \leq V/t \leq -0.5$, a BOW phase emerges for $\left|\delta t/t\right| > 0.45$, with its boundaries converging as $\left|\delta t/t\right|$ decreases, terminating at a single point at $\left|\delta t/t\right|\simeq0.45$. In other parameter regions, a CDW phase is realized. Through this analysis, we elucidate the topological properties of the interacting spinless SSH model at quarter filling, highlighting the competition among CDW, BOW, and BI phases. By tuning $V$ and $\delta t$, the system exhibits diverse correlated phenomena, offering new insights into one-dimensional quantum phase transitions and the interplay between topology and order.