Fetching the paper…

Reading the bibliography…

Entanglement negativity in quantum field theory · Around

2012

Entanglement negativity in quantum field theory

Calabrese, Pasquale, Cardy, John, Tonni, Erik

Original
PDF
Post on X

Understand

We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose rho_A^{T_2} of the reduced density matrix of a subsystem A=A1 U A2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln||\rho_A^{T_2}||.

This is shown to reproduce standard results for a pure state.
We then apply this method to conformal field theories, deriving the result E\sim(c/4) ln(L1 L2/(L1+L2)) for the case of two adjacent intervals of lengths L1, L2 in an infinite system, where c is the central charge.
For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant.

Built on

M. Bianchi, G. Pradisi, and A. Sagnotti, Nucl.Phys. B 376
1992
Earlier work this paper cites.
C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B 424
1994
Earlier work this paper cites.
P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory (Springer-Verlag, New York, 1997)
1997
Earlier work this paper cites.
K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A 58
1998
Earlier work this paper cites.
G. Vidal and R. F. Werner, Phys. Rev. A 65
2002
Earlier work this paper cites.
A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature 416
2002
Earlier work this paper cites.

Similar

K. Audenaert, J. Eisert, M. B. Plenio and R. F. Werner, Phys. Rev. A 66
2002
Cited alongside, same era.
G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90
2004
Cited alongside, same era.
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys, 80
2009
Cited alongside, same era.
P. Calabrese and J. Cardy, J. Stat. Mech. P06002 (2004); J. Phys. A 42
2009
Cited alongside, same era.
P. Calabrese, J. Cardy, and E. Tonni, J. Stat. Mech P11001 (2009)
2009
Cited alongside, same era.
H. Wichterich, J. Molina-Vilaplana, and S. Bose, Phys. Rev. A 80
2009
Cited alongside, same era.

Then

S. Marcovitch, A. Retzker, M. B. Plenio, and B. Reznik, Phys. Rev. A 80
2009
Later among the works it cites.
H. Wichterich, J. Vidal, and S. Bose, Phys. Rev. A 81
2010
Later among the works it cites.
P. Calabrese, M. Campostrini, F. Essler, and B. Nienhuis, Phys. Rev. Lett. 104
2010
Later among the works it cites.
P. Calabrese, J. Cardy, and E. Tonni, J. Stat. Mech P01021 (2011)
2011
Later among the works it cites.
S. Furukawa, V. Pasquier, and J. Shiraishi, Phys. Rev. Lett. 102
2012
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

P. Calabrese, J. Cardy, and E. Tonni, in preparation

Cited in the paper.