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Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121. For more information, contact Diego Dalvit.
December 14, 2006
Quantum Phase Transitions, Entanglment and Density Functional Theory
We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and entanglement measures. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians. 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. The theory can be based on the famous Density Functional Theory. Our general conclusions are illustrated via several quantum spin models.