Entanglement Entropy & Area Law
1D quantum chains — bipartite entanglement entropy S(l) and tensor network bond structure
Controls
Chain length L:
20
Bond dimension χ (MPS):
4
Coupling Δ (anisotropy):
1.0
State:
Critical (XX)
Recompute
Area law (1D):
S(l) ≤ const (gapped)
CFT prediction:
S(l) = (c/3)·ln[sin(πl/L)] + const
Central charge c = 1 for XX chain.
MPS bond dimension χ encodes entanglement capacity. Area law ↔ χ can be small.