Entanglement and its facets in condensed matter systems

TL;DR

This thesis explores the role of entanglement in quantum phase transitions within condensed matter systems, introduces measures for multipartite entanglement, and proposes methods for experimental detection.

Contribution

It provides a comprehensive review, new classification and quantification methods for multipartite entanglement, and links theoretical measures to experimentally accessible quantities.

Findings

Multipartite entanglement is relevant at quantum phase transitions.

A constructive SLOCC classification for multipartite qubits is developed.

Entanglement measures can be expressed via spin correlation functions.

Abstract

This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for entanglement used for this analysis. A selection of results from this research is given and proposed as evidence for the relevance of multipartite entanglement in this context. A constructive method for an SLOCC classification and quantification of multipartite qubit entanglement is outlined and results for convex roof extensions of the resulting measures are briefly discussed on a specific example. At the end, a transformation of antilinear expectation values into linear expectation values is presented which admits an expression of the aforementioned measures of genuine multipartite entanglement in terms of spin correlation function, hence making them experimentally accessible.