Quantum dynamics on a 1D spin-1/2 chain — spin wave propagation, domain walls, and entanglement spreading under the XXZ Hamiltonian.
H = -J Σ (SˣSˣ + SʸSʸ + ΔSᶻSᶻ). At Δ=0: free fermions (XX model). |Δ|<1: gapless Luttinger liquid. Δ=1: Heisenberg antiferromagnet. Δ>1: gapped Ising-like ferromagnet. Entanglement entropy grows logarithmically at criticality (Δ≤1) and saturates for Δ>1.