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arXiv:1201.4104 · Journal of Physics A Mathematical and Theoretical

Exact results for the entanglement across defects in critical chains

Ingo Peschel, Viktor Eisler

Published Mar 27, 2012• 49 citations
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Abstract

We consider fermionic and bosonic quantum chains where a defect separates two subsystems and compare the corresponding entanglement spectra. With these, we calculate their Rényi entanglement entropies and obtain analytical formulae for the continuously varying coefficient of the leading logarithmic term. For the bosonic case we also present numerical results.

DOI
10.1088/1751-8113/45/15/155301

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We consider fermionic and bosonic quantum chains where a defect separates two subsystems and compare the corresponding entanglement spectra. With these, we calculate their Rényi entanglement entropies and obtain analytical formulae for the continuously varying coefficient of the leading logarithmic term. For the bosonic case we also present numerical results.
Abstract We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the Rényi mutual information with Rényi index 1 / 2 , in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.
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