Reduced density matrices and entanglement entropy in free lattice models

By I. Peschel, V. Eisler. 2009

674 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f915f410bb8449000e90cd76ab6de0a5b3b342bc

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In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. M. Fagotti
5. V. Alba
6. J. Dubail
7. F. Essler
8. T. Nishioka

In Condensed Matter Physics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. J. Dubail
5. T. Nishioka
6. M. Fagotti
7. J. Caux
8. V. Alba

Citations in the corpus

• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “The matrix W is related to the two-point function of Majorana fermions by [123, 124, 204]”
• Entanglement dynamics after quantum quenches in generic integrable systems (2017, methodology): “For systems of free bosons, at any time after the quench the entanglement entropy of a finite subsystem can be calculated effectively [107, 108] from the time-dependent twopoint correlation functions reported in [12].”
• Entanglement of purification: from spin chains to holography (2017, methodology): “For reference, we also show the entanglement of the TFD state as an upper bound (obtained by TEBD without disentangling) and half the mutual information as a lower bound (obtained via a thermal correlation matrix method [32]).”
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d (2016, background): “For more details, see the standard references [93, 94].”
• Entanglement entropy: Holography and renormalization group (2018, methodology): “The implementation of the real time approach is described for free lattice models in (Peschel and Eisler, 2009) and for free field theories in (Casini and Huerta, 2009) that also compares the approach with the Euclidean formalism.”
• Entanglement negativity in extended systems: a field theoretical approach (2012, methodology): “Following [58, 61], we can easily relate ρA to the correlation matrices Qrs = 〈qrqs〉 and Prs = 〈prps〉 (derived above for periodic and Dirichlet boundary conditions) restricted to the part A of the system both if the subsystem is connected or formed by an arbitrary number of pieces.”
• Symmetry resolved entanglement in free fermionic systems (2019, methodology): “The corresponding RDM of the subsystem can then be written as [30–32] ρA = detCA exp (∑”