Entanglement decomposition for the simulation of quantum many-body dynamics

Nonequilibrium dynamics in quantum matter are at the frontier of current research. Efficient and precise simulation techniques are needed to improve our understanding of equilibration and thermalization, dynamical phase transitions, decoherence effects, quantum transport etc. A major obstacle is the growth of entanglement with time which generally implies an increased complexity of the quantum state. For instance, the computation costs of simulations based on tensor network states generally grow rapidly in time, limiting the maximum reachable times. I will show how this problem can be addressed through entanglement decomposition. We can follow the dynamics, starting from an initial state, until the entanglement has grown to a point where our simulation resources are exhausted. We then decompose the current state into lower entangled components and continue by simulating the evolution of these components, decomposing them again when needed. I will demonstrate a specific entanglement decomposition scheme for matrix product state simulations and discuss its efficiency for the study of dynamics in quantum magnets.