H Casini and M Huerta J. Stat. Mech. (2008) P01012 doi:10.1088/1742-5468/2008/01/P01012
H Casini and M Huerta
Show affiliationsThe trace of integer powers of the local density matrix ρV corresponding to the vacuum state reduced to a region V can be formally expressed in terms of a functional integral on a manifold with conical singularities. Recently, some progress has been made in explicitly evaluating this type of integral for free fields. However, finding the associated geometric entropy remained, in general, a difficult task involving an analytic continuation in the conical angle. In this paper, we obtain this analytic continuation explicitly, exploiting a relation between the functional integral formulas and the Chung–Peschel expressions for ρV in terms of correlators. The result is that the entropy is given in terms of a functional integral in flat Euclidean space with a cut on V where a specific boundary condition is imposed. As an example, we get the exact entanglement entropies for massive scalar and Dirac free fields in 1+1 dimensions in terms of the solutions of a nonlinear differential equation of the Painlevé V type.
E-print Number: 0707.1300
Cited: by |
Refers: to
03.67.Mn Entanglement measures, witnesses, and other characterizations
Issue 01 (January 2008)
Received 26 September 2007, accepted for publication 29 November 2007
Published 18 January 2008
H Casini and M Huerta J. Stat. Mech. (2008) P01012
Viktor Krueckl and Tobias Kramer 2009 New J. Phys. 11 093010
Jan Schwerdtfeger et al J. Stat. Mech. (2007) L04001
Tobias Kretz et al J. Stat. Mech. (2006) P02005
F H Jafarpour and S R Masharian J. Stat. Mech. (2007) P10013
Pulak Kumar Ghosh and Deb Shankar Ray J. Stat. Mech. (2007) P03003
A V Razumov and Yu G Stroganov J. Stat. Mech. (2006) P07004
Wolfgang Lechner and Christoph Dellago J. Stat. Mech. (2007) P04001
R K P Zia and B Schmittmann J. Stat. Mech. (2007) P07012
Emil J Bergholtz and Anders Karlhede J. Stat. Mech. (2006) L04001