# Visualizing elusive phase transitions with geometric entanglement

## TL;DR

This paper demonstrates that analyzing the global geometric entanglement can reveal elusive quantum phase transitions in one-dimensional spin chains, including Kosterlitz-Thouless and gapped transitions, where traditional measures fail.

## Contribution

It introduces a method to detect elusive quantum phase transitions by examining non-analyticities in geometric entanglement, providing new insights into phase transition characterization.

## Key findings

- Non-analyticities in geometric entanglement across phase transitions
- Contrast with analytic behavior of two-body reduced density operators
- Effective detection of elusive quantum phase transitions

## Abstract

We show that by examining the global geometric entanglement it is possible to identify "elusive" or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of non-analyticities in the geometric entanglement, in particular across a Kosterlitz-Thouless transition and across a transition for a gapped deformed Affleck-Kennedy-Lieb-Tasaki chain. The observed non-analyticities can be understood and classified in connection to the nature of the transitions, and are in sharp contrast to the analytic behavior of all the two-body reduced density operators and their derived entanglement measures.