Domain wall dynamics of a two dimensional quantum Ising model using tree tensor networks

Many body systems out of equilibrium are notoriously difficult to solve due to the rapid growth of entanglement with time. In particular the expanding possibilities to address two-dimensional systems in quantum simulation turn a spotlight on the lack of reliable numerical methods in this regime. We explore an approach to solve the time evolution of two-dimensional quantum systems by applying the time-dependent variational principle to Tree Tensor Networks. As an application, we consider the relaxation of domain wall initial conditions in a quantum Ising model, where pre-thermal behavior leads to a slow relaxation of domain wall initial conditions.