TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice model on a thin torus (2D), and implement the algorithm using TensorNetwork. We use a standard energy minimization procedure over a TTN ansatz with bond dimension chi, with a computational cost that scales as O(chi4). Using bond dimension chi ∈ [32,256] we compare the use of CPUs with GPUs and observe significant computational speed-ups, up to a factor of 100, using a GPU and the TensorNetwork library.