Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality

Describing nonequilibrium properties of quantum many-body systems is challenging due to high entanglement in the wave function. We describe evolution local observables via influence matrix (IM), which encodes effects a system as an environment for subsystems. Recent works found that many dynamical regimes IM infinite has low temporal and can be efficiently represented matrix-product state (MPS). Yet, direct iterative constructions encounter highly entangled intermediate states---a barrier (TEB). argue TEB ubiquitous, elucidate its physical origin semiclassical quasiparticle picture exactly captures behavior integrable spin chains. Further, we show also arises chaotic chains, lack well-defined quasiparticles. Based on these insights, formulate alternative light-cone growth algorithm, provably avoids TEB, thus providing efficient construction thermodynamic-limit MPS. This work uncovers efficiency approach studying thermalization transport.