review article · identifier verified 2026-07-29
The density-matrix renormalization group in the age of matrix product states
Ulrich Schollwöck · 2010
- Identifier
- arXiv:1008.3477
- Canonical URL
- https://arxiv.org/abs/1008.3477
Why it is in this atlas
Standard reference for MPS canonical forms, SVD truncation, and the reformulation of DMRG in tensor-network language.
Claims citing this source
- tn-001 · Established resultA 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.
- tn-003 · Established resultDMRG is understood as variational optimization over the manifold of matrix product states.
- tn-004 · Established resultTensor-network accuracy is controlled by singular-value truncation, and the discarded weight is the quantity that makes a result interpretable.
- tn-010 · Established resultTensor-network time evolution is limited by entanglement growth, which forces the bond dimension upward as the simulated time increases.