Generating function for tensor network diagrammatic summation

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting can be studied using TNs, where one however confronts the intricate summation over an extensive number diagrams. Here, we introduce a set generating functions, which encode diagrammatic summations as leading-order series expansion coefficients. Combined with automatic differentiation, function allows us to solve problem TN summation. We illustrate this scheme computing variational excited states dynamical structure factor spin chain, further investigating entanglement properties states. Extensions infinite-size higher dimension are outlined.