Concept record · edition 0.1.0
Scale invariance
Reusing the same disentangler and isometry at every layer, giving a renormalization-group transformation with no preferred length scale.
Why it matters
It matches the scale-free correlation structure of critical systems and makes the layer count grow logarithmically with system size.
Claims using this concept
- tn-005 · ConjectureThe reading of a MERA network as a discretized holographic geometry is a proposed correspondence, not a derived one, and published work argues its consistency conditions are in tension.
- tn-006 · Established resultMERA introduces disentanglers before coarse-graining, allowing it to reproduce the entanglement scaling of critical systems that a tree tensor network cannot.
Sources
primary paper · identifier verified
A class of quantum many-body states that can be efficiently simulated
G. Vidal · 2006
arXiv:quant-ph/0610099
Primary source for the MERA ansatz and its efficient contraction, including the scale-invariant construction.
Source record →review article · identifier verified
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
Román Orús · 2013
arXiv:1306.2164
Review covering tensor-network structure, entanglement scaling, and contraction strategy; the general reference for this atlas.
Source record →