Comparing the Capabilities of Time-Evolution Methods for Tree Tensor Networks

We compare the performance of the usual project splitting time-dependent variational principle with the novel basis update and Galerkin method for tree tensor network simulations. The tensor network framework has been used successfully to simulate many-body quantum systems, and current research looks to extend the capabilities by using tree tensor networks. One of these capabilities is simulating the time evolution of many-body quantum systems, for which the two above methods were developed. We use both methods to simulate a variety of quantum systems, such as Ising models on different topologies and dissipative Bose Hubbard models, in order to evaluate the capabilities of both methods. We focus especially on the ability to adapt the tensor network bond dimension dynamically and the capability to simulate open quantum systems, such as the above-mentioned Bose-Hubbard model.