dorsal/arxiv
View SchemaQuantum Phase Transitions and Bipartite Entanglement
| Authors | Lian-Ao Wu, Marcelo S. Sarandy, Daniel A. Lidar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407056 |
| URL | https://arxiv.org/abs/quant-ph/0407056 |
| DOI | 10.1103/PhysRevLett.93.250404 |
| Journal | Phys. Rev. Lett. 93, 250404 (2004) |
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.
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"abstract": "We develop a general theory of the relation between quantum phase transitions\n(QPTs) characterized by nonanalyticities in the energy and bipartite\nentanglement. We derive a functional relation between the matrix elements of\ntwo-particle reduced density matrices and the eigenvalues of general two-body\nHamiltonians of $d$-level systems. The ground state energy eigenvalue and its\nderivatives, whose non-analyticity characterizes a QPT, are directly tied to\nbipartite entanglement measures. We show that first-order QPTs are signalled by\ndensity matrix elements themselves and second-order QPTs by the first\nderivative of density matrix elements. Our general conclusions are illustrated\nvia several quantum spin models.",
"arxiv_id": "quant-ph/0407056",
"authors": [
"Lian-Ao Wu",
"Marcelo S. Sarandy",
"Daniel A. Lidar"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevLett.93.250404",
"journal_ref": "Phys. Rev. Lett. 93, 250404 (2004)",
"title": "Quantum Phase Transitions and Bipartite Entanglement",
"url": "https://arxiv.org/abs/quant-ph/0407056"
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