4.8 Article

Quantum phase transitions and bipartite entanglement

Journal

PHYSICAL REVIEW LETTERS
Volume 93, Issue 25, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.93.250404

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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.

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