# Bipartite charge fluctuations in one-dimensional $\mathbb{Z}_2$ superconductors and insulators

## TL;DR

This paper investigates bipartite charge fluctuations in one-dimensional topological models, revealing their effectiveness in detecting phase transitions and topological invariants, including at critical points with universal logarithmic contributions.

## Contribution

It demonstrates how BCF can identify topological phase transitions and invariants in non-conserving charge models, extending previous methods to a broader class of systems.

## Key findings

- BCF detect topological phase transitions via winding number changes
- A universal logarithmic term appears at critical points
- Results apply to various models including Kitaev, SSH, and Rashba nanowires

## Abstract

Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems). In this Letter, we study the BCF in generic one-dimensional $\mathbb{Z}_2$ (topological) models including the Kitaev superconducting wire model, the Ising chain or various topological insulators such as the SSH model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the XYZ model.