Partial time-reversal transformation and entanglement negativity in fermionic systems
By Hassan Shapourian, Ken Shiozaki, S. Ryu. 2016
141 citations recorded by the source corpus.
The partial transpose of density matrices in many-body quantum systems, in which one takes the transpose only for a subsystem of the full Hilbert space, has been recognized as a useful tool to diagnose quantum entanglement. It can be used, for example, to define the (logarithmic) negativity. For fermionic systems, it has been known that the partial transpose of Gaussian fermionic density matrices is not Gaussian. In this work, we propose to use partial time-reversal transformation to define (an analog of) the entanglement negativity and related quantities. We demonstrate that for the symmetry-protected topological phase realized in the Kitaev chain the conventional definition of the partial transpose (and hence the entanglement negativity) fails to capture the formation of the edge Majorana fermions, while the partial time-reversal computes the quantum dimension of the Majorana fermions. Furthermore, we show that the partial time-reversal of fermionic density matrices is Gaussian and can be computed efficiently. Various results (both numerical and analytical) for the entanglement negativity using the partial-time reversal are presented for (1+1)-dimensional conformal field theories, and also for fermionic disordered systems (random single phases).
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/064a069d30d4dfb6f8561fbe40be1348d019b907
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In Artificial Intelligence
- R. Bonsignori
- Paola de Ruggiero
- Pasquale Calabrese
- T. Takayanagi
- J. Cardy
- Thomas Hartman
- T. Nishioka
- E. Tonni
In Atomic and Molecular Physics, and Optics
- R. Bonsignori
- Paola de Ruggiero
- Pasquale Calabrese
- J. Cardy
- E. Tonni
- T. Takayanagi
- T. Nishioka
- Thomas Hartman
Citations in the corpus
- Symmetry resolved entanglement in free fermionic systems (2019, background): “Moreover, similar quantities have also been introduced in the holographic setting [21,22] and in the study of entanglement in mixed states [15,24,25].”