Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition
arXiv:1303.1623 · doi:10.1103/PhysRevA.88.012310
Abstract
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.
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- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Scaling of genuine multiparticle entanglement at a quantum phase transition
- Measuring multipartite quantum correlations by thermodynamic work extraction
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- Entanglement duality in spin-spin interactions