Claim record · edition 0.1.0
DMRG is understood as variational optimization over the manifold of matrix product states.
The density-matrix renormalization group was formulated before the tensor-network language existed; the later reformulation showed the states it produces are matrix product states and its sweeps are variational updates on them.
Limits of this claim
The reformulation is a change of description, not of results. It does not by itself extend DMRG's reach beyond the regimes where it already worked.
Supporting sources
primary paper · identifier verified
Density matrix formulation for quantum renormalization groups
Steven R. White · 1992
DOI:10.1103/PhysRevLett.69.2863
Primary source for DMRG, the variational method later understood as optimization over matrix product states.
Source record →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 →