Related Experiment Video
Updated: Aug 15, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Quantum phase transitions and bipartite entanglement
L-A Wu1, M S Sarandy, D A Lidar
1Chemical Physics Theory Group, Department of Chemistry, Center for Quantum Information and Quantum Control, University of Toronto, Ontario M5S 3H6, Canada.
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.
Related Concept Videos
Phase Transitions
Phase Diagram
Entropy Changes Accompanying Specific Processes
Phase Transitions
The Phase Rule
Phase Diagram

