Probing Topological Phases in a Strongly Correlated Ladder Model via Entanglement

TL;DR

This study explores how strong electronic interactions affect topological phases in a ladder model, revealing that some topological features are robust while others are significantly altered by interactions.

Contribution

It provides the first detailed phase diagram of a strongly correlated ladder model with topological properties using entanglement measures.

Findings

Topological phase remains stable at its non-interacting location despite interactions.

Edge entanglement entropy changes non-trivially with interactions.

Phase boundary for winding number one shifts significantly with increasing interaction.

Abstract

The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between the legs. This model hosts a symmetry-protected topological phase in its non-interacting limit. Using the density-matrix renormalisation group algorithm, we compute the comprehensive quantum phase diagram in the presence of a repulsive inter-leg density-density interaction. Our analysis, based on entanglement entropy and the entanglement spectrum, reveals a fascinating dichotomy in the stability of the topological phase. We find a non-trivial change in the value of the edge entanglement entropy as we include interaction. Furthermore, we find that the phase boundary separating a trivial insulator phase and a topological one with winding number two remains robustly pinned at its non-interacting location, irrespective of the interaction strength. Variation of the effective conformal field theory's central charge near the critical line explains the robustness of the gap. In contrast, the transition to an insulating phase with winding number one is heavily renormalised, with the critical line shifting significantly as the interaction increases. By successfully mapping the phase diagram and identifying the distinct behaviours of the phase boundaries, our work clarifies how interactions can selectively preserve or destroy different aspects of a topological phase.