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

TL;DR

The paper investigates a one-dimensional spinless SSH model at quarter filling with nearest-neighbor interactions to understand how topology and correlation-driven order compete. Using exact diagonalization with twisted boundary conditions and complementary mean-field analyses, it maps a phase diagram featuring a topologically trivial band insulator (BI), a bond-order wave (BOW), and a charge-density wave (CDW), with critical boundaries around $V/t\approx-2.3$ and $|\delta t/t|\approx0.45$. The study employs multiple diagnostics, including gaps, structure factors, real-space occupancies, and entanglement, to identify phase transitions and the dominance of order parameters, complemented by momentum-space correlations. The work highlights the interplay between topology and order in 1D correlated systems and demonstrates how topology can coexist with, or be masked by, symmetry-breaking phases in low dimensions.

Abstract

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 $\left|δt/t\right| > 0.45$, with its boundaries converging as $\left|δt/t\right|$ decreases, terminating at a single point at $\left|δt/t\right|\simeq0.45$. 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 $δt$, the system exhibits diverse correlated phenomena, offering new insights into one-dimensional quantum phase transitions and the interplay between topology and order.

Figures (15)

• Figure 1: The distribution of the particle-hole energy gap $\Delta_{ph}$ in the parameter space $(\delta t, V)$ reveals the metal-insulator transition of the system. At $V = 0$, $\Delta_{ph}$ vanishes, indicating a gapless metallic phase. As the interaction strength $V$ increases, $\Delta_{ph}$ becomes finite, signaling the onset of an insulating phase characterized by a finite excitation gap. The occurrence of negative values of $\Delta_{ph}$ in the figure originates from finite-size effects. And the expression used to calculate $\Delta_{ph}$ here is derived from Eq. \ref{['eq3']}.
• Figure 2: Schematic representation of the Hamiltonian (a); and (b) presented is the ground-state phase diagram of this one-dimensional SSH model at quarter filling.
• Figure 3: Panel $\left(a\right)$ displays the distribution of the energy gap $\Delta$ in the parameter space of $\left(\delta t,V\right)$.Panel $\left(b\right)$ shows the variation of $\Delta$ as a function of $V/t$ for fixed values of $\delta t/t$. The data were computed at quarter filling with a lattice size of $L=16$.
• Figure 4: The distribution of the derivative of the energy gap $\Delta$ with respect to $V$ in the parameter space $\left(\delta t,V\right)$.
• Figure 5: $\left(a\right)$ shows the distribution of the CDW structure factor $S_{cdw}$ in the parameter space $\left(\delta t,V\right)$ ; and $\left(b\right)$ shows the distribution of $S_{\nu N}$.