Geometric mutual information at classical critical points.
A practical use of the entanglement entropy in a 1D quantum system is to identify the conformal field theory describing its critical behavior. It is exactly (c/3)lnℓ for an interval of length ℓ in an infinite system, where c is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2D conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to c. This makes it possible to extract c in classical simulations, which we demonstrate for the critical Ising and three-state Potts models.
Physics Department, University of Virginia, Charlottesville, Virginia 22904-4714, USA.
Jean-Marie
JM
Stéphan
Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada.
Stephen
S
Inglis
Physics Department, University of Virginia, Charlottesville, Virginia 22904-4714, USA.
Paul
P
Fendley
Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Roger G
RG
Melko