Reduced density matrices and entanglement entropy in free lattice models

2009/06/30 by Ingo Peschel, Viktor Eisler · 3 citations
Physics and Astronomy · #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1088/1751-8113/42/50/504003

published as J. Phys. A: Math. Theor. 42 504003 (2009) · 33 pages, 18 figures, minor changes, references added. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A

arxiv created 2009/09/01 · arxiv updated 2015/05/13

Abstract

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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