Quantum Phase Transitions and Bipartite Entanglement

Wu, Lian-Ao; Sarandy, Marcelo S.; Lidar, Daniel A.

Quantum Phase Transitions and Bipartite Entanglement

Authors

Wu, Lian-Ao

Sarandy, Marcelo S.

Lidar, Daniel A.

Description

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.
5 pages, incl. 2 figures. v3: The version published in PRL, including a few extra comments and clarifications for which there was no space in the PRL