3 research outputs found
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure
Reduced density matrices and entanglement entropy in free lattice models
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.Comment: 33 pages, 18 figures, minor changes, references added. Review article
for the special issue "Entanglement entropy in extended systems" in J. Phys.
A short review on entanglement in quantum spin systems
We review some of the recent progress on the study of entropy of entanglement
in many-body quantum systems. Emphasis is placed on the scaling properties of
entropy for one-dimensional multi-partite models at quantum phase transitions
and, more generally, on the concept of area law. We also briefly describe the
relation between entanglement and the presence of impurities, the idea of
particle entanglement, the evolution of entanglement along renormalization
group trajectories, the dynamical evolution of entanglement and the fate of
entanglement along a quantum computation.Comment: 20 pages and 6 figures. Review article for the special issue
"Entanglement entropy in extended systems" in J. Phys. A, edited by P.
Calabrese, J. Cardy and B. Doyo