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.

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.