Entanglement entropy as a probe of topological phase transitions

TL;DR

This paper introduces an entanglement entropy-based method to identify topological phase transitions in disordered systems, demonstrating its effectiveness in SSH models with various disorder types.

Contribution

The authors develop an exact EE framework that detects topological transitions even with disorder, outperforming some traditional invariants in certain cases.

Findings

EE difference $ riangle S^{ ext{A}}$ vanishes in topological phase, remains finite in trivial phase.

The method accurately determines phase boundaries using Lyapunov exponents and transfer matrices.

EE-based diagnostics remain effective in the presence of quasiperiodic or binary disorder.

Abstract

Entanglement entropy (EE) provides a powerful probe of quantum phases, yet its role in identifying topological phase transitions in disordered systems remains underexplored. We introduce an exact EE-based framework that captures topological phase transitions even in the presence of disorder. Specifically, for a class of Su-Schrieffer-Heeger (SSH) model variants, we show that the difference in EE between half-filled and near-half-filled ground states, $\Delta S^{\mathcal{A}}$, vanishes in the topological phase but remains finite in the trivial phase, a direct consequence of edge-state localization. This behavior persists even in the presence of quasiperiodic or binary disorder. By analyzing domain-wall configurations in the SSH chain, we further show how subsystem tuning allows one to distinguish genuine topological zero-energy eigenstates from trivial localized states. Exact phase boundaries, derived from Lyapunov exponents via transfer matrices, agree closely with numerical results from $\Delta S^{\mathcal{A}}$ and the topological invariant $\mathcal{Q}$, with instances where $\Delta S^{\mathcal{A}}$ outperforms $\mathcal{Q}$. Our results highlight EE as a robust diagnostic tool and a potential bridge between quantum information and condensed matter approaches to topological matter.