Claim record · edition 0.1.0
A matrix product state represents a many-body state with a cost controlled by its bond dimension, which bounds the entanglement it can carry across any cut.
The bond dimension D fixes the variational manifold. Because an MPS of bond dimension D carries at most log(D) entanglement entropy across a cut, the representation is efficient precisely when the target state's entanglement is bounded.
Limits of this claim
This is a statement about representational capacity, not a guarantee that any particular state of interest is reachable at a practical D.
Supporting sources
review article · identifier verified
The density-matrix renormalization group in the age of matrix product states
Ulrich Schollwöck · 2010
arXiv:1008.3477
Standard reference for MPS canonical forms, SVD truncation, and the reformulation of DMRG in tensor-network language.
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 →