Entanglement, dynamical bifurcations and quantum phase transitions

Andrew P. Hines

Published Jan 1, 2005• 2 citations

Abstract

Entanglement is a principle concept in quantum information science and is central to an understanding of complex behaviour in strongly interacting, quantum many-body systems. This thesis applies the quantitative theory of entanglement to analyse composite quantum systems. We attempt to provide a simplified approach to quantum phase transitions in the context of dynamical bifurcations.We consider the entanglement in the ground state of quantum systems with well-defined semiclassical analogues. In particular, we are interested in semiclassical models that exhibit bifurcations of stationary points. We introduce previously unknown connections between the entanglement in the ground state of such quantum models and the bifurcations in the corresponding semiclassical limit. In the case of many body systems, the change in ground state entanglement at dynamical instabilities is related to the phenomenon of quantum phase transitions.By investigating the ground state entanglement in a number of representative quantum systems, a connection between dynamical bifurcations and quantum phase transitions facilitated by the entanglement is demonstrated. The interrelationships between the three phenomena have the potential to facilitate a more general understanding of quantum phase transitions.

DOI: 10.14264/107517

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