Disorder-driven MBL phase: logarithmic vs. volume-law entanglement entropy
In the many-body localized phase (disorder W > W_c ~ 3.5 for XXZ chain), entanglement entropy grows logarithmically in time S(t) ~ log(t) rather than linearly (thermal phase). Visualized: density matrix diagonal and off-diagonal elements (entanglement spreading), real-space density profile, and entanglement entropy vs time comparison between ergodic and MBL regimes.