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 (15)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Entanglement and the Phase Transition in Single Mode Superradiance
• Entanglement versus Correlations in Spin Systems
• A subsystem-independent generalization of entanglement
• Entanglement in a second order quantum phase transition
• Entanglement, quantum phase transition and scaling in XXZ chain
• Entanglement in a first order quantum phase transition
• Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models
• Nature and Measure of Entanglement in Quantum Phase Transitions
• Macroscopic entanglement jumps in model spin systems
• Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls

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