Quantum phase transitions and bipartite entanglement.
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.
Wu
L-A
LA
Chemical Physics Theory Group, Department of Chemistry, Center for Quantum Information and Quantum Control, University of Toronto, Ontario M5S 3H6, Canada.
Sarandy
M S
MS
Lidar
D A
DA