Partial time-reversal transformation and entanglement negativity in fermionic systems

Journal Article · Mon Apr 03 00:00:00 EDT 2017 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.95.165101· OSTI ID:1535897

Shapourian, Hassan ^[1]; Shiozaki, Ken ^[1]; Ryu, Shinsei ^[1]

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1. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics

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, 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).

• Research Organization: Univ. of Illinois at Urbana-Champaign, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0008692
• OSTI ID: 1535897
• Alternate ID(s): OSTI ID: 1349701
• Journal Information: Physical Review. B, Vol. 95, Issue 16; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English