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 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. Our general conclusions are illustrated via several quantum spin models.

5 pages, incl. 2 figures. v3: The version published in PRL, including a few extra comments and clarifications for which there was no space in the PRL

References in corpus (1)

• Entanglement in a first order quantum phase transition

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• Entanglement and Quantum Phase Transition Revisited
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• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Thermal entanglement properties of small spin clusters
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions