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Quantum Phase Transitions and Bipartite Entanglement

Lian-Ao Wu·Marcelo S. Sarandy·Daniel A. Lidar
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Abstract

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of $d$-level systems. The ground state energy eigenvalue and its derivatives, whose non-analyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signalled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.

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Lian-Ao Wu, Marcelo S. Sarandy, Daniel A. Lidar. 2004-12-17. Quantum Phase Transitions and Bipartite Entanglement. https://doi.org/10.1103/physrevlett.93.250404

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