title: Quantum phase transitions and bipartite entanglement.
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 nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled 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.
authors.affiliation: Chemical Physics Theory Group, Department of Chemistry, Center for Quantum Information and Quantum Control, University of Toronto, Ontario M5S 3H6, Canada.
authors.forename: L-A
authors.initials: LA
authors.lastname: Wu
authors.forename: M S
authors.initials: MS
authors.lastname: Sarandy
authors.forename: D A
authors.initials: DA
authors.lastname: Lidar