Reduced density matrices and entanglement entropy in free lattice models

Details Reduced density matrices and entanglement entropy in free lattice models Reduced density matrices and entanglement entropy in free lattice models

2009-06-09

arxiv.org/abs/0906.1663v3

J. Phys. A: Math. Theor. 42 504003 (2009)

Physics

Condensed Matter

Statistical Mechanics

33 pages, 18 figures, minor changes, references added. Review article for the special issue "Entanglement entropy in extended

Scientific paper

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and the full spectra, the resulting entanglement and in particular the entanglement entropy. This is done for various one- and two-dimensional situations, including also the evolution after global or local quenches.

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