Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Exact results for the entanglement across defects in critical chains

Ingo Peschel, Viktor Eisler

Published Jan 1, 2012• 49 citations
Publisher

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
10.17169/refubium-18921

Related papers

Exact results for the entanglement across defects in critical chains

Ingo Peschel, Viktor Eisler

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.

arXiv:1201.4104•Journal of Physics A Mathematical and Theoretical•Mar 27, 2012•49 citations

Entanglement in fermionic chains with interface defects

Viktor Eisler, Ingo Peschel

Abstract We study the ground‐state entanglement of two halves of a critical transverse Ising chain, separated by an interface defect. From the relation to a two‐dimensional Ising model with a defect line we obtain an exact expression for the continuously varying effective central charge which governs the asymptotic behaviour of the entanglement entropy. The result is relevant also for other fermionic chains.

arXiv:1005.2144•Annalen der Physik•Jul 19, 2010•79 citations

On entanglement evolution across defects in critical chains

Viktor Eisler, Ingo Peschel

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground- state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.

•Jan 1, 2012•36 citations

On entanglement evolution across defects in critical chains

Viktor Eisler, Ingo Peschel

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.

arXiv:1205.4331•Europhysics Letters (EPL)•Jul 1, 2012•82 citations

Entanglement negativity in a fermionic chain with dissipative defects: exact results

Fabio Caceffo, Vincenzo Alba

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.

arXiv:2209.14164•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2023•18 citations

Entanglement Hamiltonians for non-critical quantum chains

Viktor Eisler, Giuseppe Di Giulio, Erik Tonni C +1 more

Abstract We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

arXiv:2007.01804•Journal of Statistical Mechanics Theory and Experiment•Oct 1, 2020•43 citations
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.
Abstract We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.