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Quantum Entanglement in Second-quantized Condensed Matter Systems
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.Comment: 11 pages. Journal versio