Quantum phase transition in spin systems studied through entanglement estimators

TL;DR

This paper investigates how entanglement, measured by concurrence, relates to quantum phase transitions in spin systems modeled by Heisenberg-like Hamiltonians on chains and lattices.

Contribution

It clarifies the relationship between entanglement estimators and quantum phase transitions in spin systems, focusing on the role of concurrence in these phenomena.

Findings

Concurrence can be related to correlators in $S=1/2$ systems.

Entanglement shows distinct behavior near quantum critical points.

The study enhances understanding of entanglement's role in quantum phase transitions.

Abstract

Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of entangled states can be easily verified, the quantitative estimate of this property is still under investigation. One of the most useful tool in this framework is the concurrence whose definition, albeit limited to $S=1/2$ systems, can be related to the correlators. We consider quantum spin systems defined along chains and square lattices, and described by Heisenberg-like Hamiltonians: our goal is to clarify the relation between entanglement and quantum phase transitions, as well as that between the concurrence the and the specific quantum state of the system.