I've been wondering about why tensor networks are capable of avoiding MC sign problem (e.g. see arXiv:1611.04791 [hep-lat] and the references therein). I have seen many papers stating that the TNs are very useful to avoid sign problem but could not find proof or a reference to the proof. Does anyone know why TNs can be used to avoid sign problem or have any reference to prove?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Tensor networks are good at taking symmetries and rules into account, by enforcing particular constraints on the individual tensors. These slides (or the accompanying paper) explain how the sign problem is avoided in the case of 2D fermionic systems, by explicitly constraining each tensor to be parity preserving, and replacing leg crossings with antisymmetric swap tensors.
Overall, tensor networks are mainly limited by the entanglement scaling of the system (area law vs volume law). So long as the bond dimension required by this is small, they can carry out whatever fancy combinatorics you like.
