Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains

1997/10/29 by J. Dukelsky, J Dukelsky, M. A. Martin-Delgado +5 · 7 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Density matrix renormalization group #Equivalence (formal languages) #Invariant (physics) #Matrix multiplication #Matrix product state #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum many-body systems #Spin (aerodynamics) #Spin density #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1209/epl/i1998-00381-x

REVTEX file, 4 pages, NO figures inserted in text. 2 Tables

arxiv created 1997/10/29 · openalex publication_date 1998/08/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the relationship between the Density Matrix Renormalization Group (DMRG) and the variational matrix product method (MPM). In the latter method one can also define a density matrix whose eigenvalues turn out to be numerically close to those of the DMRG. We illustrate our ideas with the spin-1 Heisenberg chain, where we compute the ground-state energy and the spin correlation length. We also give a rotational invariant formulation of the MPM.

Citations

• Density-matrix algorithms for quantum renormalization groups

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