# Quantum Phase Transition and Entanglement in Topological Quantum Wires

## TL;DR

This paper studies quantum phase transitions in topological quantum wires, revealing that local entanglement nonanalyticities signal topological changes and uncovering a new entanglement pattern transition independent of spectral gap closure.

## Contribution

It demonstrates that local entanglement nonanalyticities universally characterize topological phase transitions in one-dimensional noninteracting fermion systems and identifies a novel entanglement pattern transition.

## Key findings

- Local entanglement becomes discontinuous at topological phase transitions.
- Universal nonanalyticity observed in SSH and Kitaev chain models.
- A new phase transition identified by entanglement pattern change, independent of spectral gap closure.

## Abstract

We investigate the quantum phase transition of the Su-Schrieffer-Heeger (SSH) model by inspecting the two-site entanglements in the ground state. It is shown that the topological phase transition of the SSH model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this nonanalyticity has a topological origin. Such a peculiar singularity has a universal nature in one-dimensional topological phase transitions of noninteracting fermions. We make this clearer by pointing out that an analogous quantity in the Kitaev chain exhibiting the identical nonanalyticity is the local electron density. As a byproduct, we show that there exists a different type of phase transition, whereby the pattern of the two-site entanglements undergoes a sudden change. This transition is characterised solely by quantum information theory and does not accompany the closure of the spectral gap. We analyse the scaling behaviours of the entanglement in the vicinities of the transition points.