Quantum many-body dynamics of ultracold . . .

We study complex quantum many-body dynamics of ultracold bosons in one-dimensional optical lattice potentials. Until recently, reliable time-dependent simulation of these systems was limited due to exponential growth of the Hilbert space with the size of the quantum system. However, in 2003-2004, G. Vidal devised the time-evolving block decimation algorithm: a time-adaptive density matrix renormalization group routine with roots in quantum information theory that allows efficient quasi-exact classical simulation of one-dimensional quantum many-body systems exhibiting a limited amount of entanglement. We apply these algorithms to the Bose-Hubbard Hamiltonian, a truncation of the full many-body Hamiltonian in second quantization that accurately describes the physics of ultracold bosons in deep optical lattices. Specifically, we study dark solitons, self-sustaining nonlinear waves that are observed throughout nature and are an emergent property of Bose-Einstein condensates in the mean-field limit; we treat solitons in the fully quantum many-body setting o