Tensor network methods with automatic differentiation

While the recent development for projected entangled-pair states (PEPS) has demonstrated its capability in studying the ground states of two-dimensional quantum many-body systems, properties of quasiparticle excitations are still cumbersome to compute. The key bottleneck for this computation is the summation of infinitely many tensor diagrams. The way we solve this problem is to represent the tensor diagram summations as a suitably defined generating function for PEPS. This is possible due to locality of many-body systems and the fact that low-energy excitations only contain one or few quasiparticles. Taking a physically motivated form for excited states, we show that relevant objects in determining excitations can be expressed as derivatives of a single tensor diagram and thus can be efficiently computed. With excited states available, dynamical correlations can also be conveniently computed. We hope that, through the adoption of tensor network generating functions, many physical properties can be more easily obtained with the tensor network algorithm.