Entangled Dynamics of the Transverse Quantum Ising Model at Finite Temperature*

An outstanding question in entangled dynamics of quantum phase transitions is the role of finite temperature. We study this problem in the context of ultracold molecules in optical lattices, which exhibit the tranverse quantum Ising model. We use both time-dependent matrix product density operator (MPDO) and matrix-product-state (MPS) methods based on tensor networks to compare zero and finite temperature dynamics, the latter represented by the Gibbs distribution. Explorations include local and global quantum quenches and the spreading of correlations.