Projected entangled-pair states (PEPS) provide excellent variational wave functions for ground of strongly correlated quantum systems in two dimensions. Determining the expectation value such a PEPS function requires contraction two-dimensional tensor network. Here, authors show that this can itself be formulated as problem, allowing one to compare accuracies commonly used schemes. The find goo...

We prove the existence of a weak solution for boundary value problems driven by mixed local--nonlocal operator. The main novelty is that such an operator allowed to be nonpositive definite.