Matrix Product States & Entanglement

Matrix product states (MPS/tensor trains) efficiently represent weakly entangled quantum states. The bond dimension χ controls expressiveness — area-law ground states need only polynomial χ. This visualization shows the entanglement entropy across all bipartitions for different quantum states, alongside the MPS tensor network diagram.

Sites N 12 Bond dim χ 4 Coupling J 1.0 Field h 0.5

Entanglement entropy S(A) = -Tr(ρ_A log ρ_A) across all bipartitions. Area-law states have S = O(1); volume-law states S = O(n).