dorsal/arxiv
View SchemaQuantum Entanglement in Second-quantized Condensed Matter Systems
| Authors | Yu Shi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204058 |
| URL | https://arxiv.org/abs/quant-ph/0204058 |
| DOI | 10.1088/0305-4470/37/26/014 |
| Journal | J. Phys. A 37, 6807 (2004) |
Abstract
The entanglement between occupation-numbers of different single particle basis states depends on coupling between different single particle basis states in the second-quantized Hamiltonian. Thus in principle, interaction is not necessary for occupation-number entanglement to appear. However, in order to characterize quantum correlation caused by interaction, we use the eigenstates of the single-particle Hamiltonian as the single particle basis upon which the occupation-number entanglement is defined. Using the proper single particle basis, we discuss occupation-number entanglement in important eigenstates, especially ground states, of systems of many identical particles. The discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation, and the electron-hole entanglement in excitations. The entanglement in a quantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper fractional part of the filling factor. For BCS superconductivity, the entanglement is a function of the relative momentum wavefunction of the Cooper pair, and is thus directly related to the superconducting energy gap. For a spinless Bose system, entanglement does not appear in the Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov theory.
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"abstract": "The entanglement between occupation-numbers of different single particle\nbasis states depends on coupling between different single particle basis states\nin the second-quantized Hamiltonian. Thus in principle, interaction is not\nnecessary for occupation-number entanglement to appear. However, in order to\ncharacterize quantum correlation caused by interaction, we use the eigenstates\nof the single-particle Hamiltonian as the single particle basis upon which the\noccupation-number entanglement is defined. Using the proper single particle\nbasis, we discuss occupation-number entanglement in important eigenstates,\nespecially ground states, of systems of many identical particles. The\ndiscussions on Fermi systems start with Fermi gas, Hatree-Fock approximation,\nand the electron-hole entanglement in excitations. The entanglement in a\nquantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper\nfractional part of the filling factor. For BCS superconductivity, the\nentanglement is a function of the relative momentum wavefunction of the Cooper\npair, and is thus directly related to the superconducting energy gap. For a\nspinless Bose system, entanglement does not appear in the\nHatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov\ntheory.",
"arxiv_id": "quant-ph/0204058",
"authors": [
"Yu Shi"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1088/0305-4470/37/26/014",
"journal_ref": "J. Phys. A 37, 6807 (2004)",
"title": "Quantum Entanglement in Second-quantized Condensed Matter Systems",
"url": "https://arxiv.org/abs/quant-ph/0204058"
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