Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model

TL;DR

This paper investigates quantum phase transitions in the transverse field Ising model across one, two, and three dimensions using multi-partite entanglement measures, revealing universal features and the effectiveness of global entanglement as a transition indicator.

Contribution

It demonstrates that global entanglement effectively signals quantum phase transitions and exhibits universal behavior across different dimensions in the Ising model.

Findings

Global entanglement indicates quantum phase transitions.

Universal features of multi-partite entanglement across dimensions.

Finite-size scaling yields critical points and exponents.

Abstract

In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric GHZ-like state to a paramagnetic product-state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one and two dimensional models. Our results indicate that such multi-partite measure of global entanglement shows universal features regardless of dimension $d$. Our results also provides evidence that multi-partite entanglement is better suited for the study of quantum phase transitions than the much studied bi-partite measures.