Is there a simple way to calculate bipartite entanglement entropy for 2D system?

Question

Suppose, we bipartite the system in the middle in two equal half. In that case, is there any simple way to calculate EE like 1d system?

Answer 1

Hi, so yes you can calculate this kind of entanglement (I assume you mean using DMRG to first compute a ground-state MPS of a 2D system?).

The way to do it is to arrange the numbering of your sites to first visit every site in the left half of your system, then every site in the right half. If you do the "zig zag" path of an MPS through a 2D cylinder or rectangle this property will already be fulfilled.

Then simply compute the entanglement entropy the same way you would for a 1D system, cutting on the bond that separates the two halves of your system.

http://itensor.org/docs.cgi?page=formulas/entanglement_mps

Here are some related questions and answers:
http://itensor.org/support/74/how-to-define-and-implement-a-zig-zag-chain?show=80#a80
http://itensor.org/support/580/entanglement-entropy-of-2d-mps?show=580#q580

Best regards,
Miles