Coupling induced emergent topology in a two-leg fermionic ladder

TL;DR

This work analyzes spinless fermions on a two-leg ladder with one SSH-dimerized leg and one uniform-leg, uncovering robust topology induced by inter-leg coupling at half-filling. The non-interacting regime exhibits a topological phase for any finite inter-leg hopping, with a boundary at $t_p=\sqrt{2t(t_1+t_2)}$ where the gap closes and the Berry phase changes; a reversal of Thouless pumping occurs when the dimerization pattern is switched. Introducing rung interactions $V_p$ yields an interaction-driven topological phase transition, confirmed by Berry-phase changes, edge-state signatures, entanglement spectra, and string-order correlations. When uniform interactions are present on all bonds, the system no longer supports the topological phase and instead undergoes a transition to a bond-ordered or charge-density wave state, described by local order parameters rather than topology. These results highlight how lattice geometry, inter-chain coupling, and fermionic statistics jointly stabilize or suppress topological order in quasi-1D systems, with potential extensions to other ladder geometries and interacting platforms.

Abstract

We investigate the ground state properties of spinless fermions on a two leg ladder, by allowing the nearest-neighbour hopping dimerization in one leg and uniform hopping in the other. In the non-interacting limit, we find that, at half-filling, the system exhibits robust topological behavior if the inter-leg hopping is allowed. Though depending on the dimerization pattern, the dimerized leg can be either topological or trivial in nature, here we show that by connecting such a leg to a uniform leg through inter-chain coupling, the overall system becomes topological irrespective of the dimerization pattern in the dimerized leg. As a result, a topological phase transition occurs as a function of the inter-leg hopping. When the inter-leg interaction is turned on, the topological phase survives, and we obtain an interaction induced topological phase transition. Finally, we reveal that when uniform interactions are included on all the bonds of the ladder, the topological phase transitions to a symmetry-broken charge-density wave (CDW) phase.

Figures (15)

• Figure 1: Schematic of a two-leg ladder with dimerized hopping along the upper leg. The circles denote lattice sites. The alternating hopping amplitudes are $t_1$ and $t_2$, where the stronger hopping is represented by thick solid lines and the weaker hopping by thin solid lines. The lower leg has uniform hopping, shown by thick solid lines. Panel (a) corresponds to $t_1<t_2$, while panel (b) corresponds to $t_1>t_2$.
• Figure 2: The left panels in (a-d) represent the single particle dispersion bands for $t_p=0.0,~0.8,~\sqrt{2.4},~\text{and}~2.5$ respectively. The right panels in (a-d) represent the corresponding particle filling ($\rho$) plotted against the chemical potential ($\mu$) for the same values of $t_p$ with a system of $L=500$ rungs. For all the plots, the values of $t_1$ and $t_2$ are fixed at $0.2$ and $1.0$ respectively.
• Figure 3: (a) and (b) energy spectrum as a function of rung hopping $t_p$ when $t_1=0.2$, $t_2 = 1.0$ and $t_1=1.0$, $t_2 = 0.2$ respectively. (c) and (d) represent the probability density $|{\psi_i}|^2$, where the circles represent the sites of the ladder and the facecolor of the circle represents the probability density corresponding to the blue circle in (a) and (b), respectively.
• Figure 4: (a) and (b) illustrate winding number as a function of $t_p$ when $t_1=0.2$, $t_2=1.0$ and $t_1=1.0$, $t_2=0.2$, respectively.
• Figure 5: The phase diagram in the $t_p-t_1$ plane is shown for $t_2=1.0$. In panel (a), the color bar represents the single-particle excitation gap ($G$) at half-filling, computed for a system of size $L=480$ under OBC. In panel (b), the blue regions correspond to a winding number $\omega/\pi=1$ and gray regions to $\omega/\pi=0$ obtained under PBC. The horizontal lines at $t_1=t_2=1.0$ indicate the gapless line.