Claim record · edition 0.1.0

tn-003Established result

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.

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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 →

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