Matrix product representations for all valence bond states

2007/12/31 by Vahid Karimipour, Laleh Memarzadeh · 4 citations
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.77.094416

published as Phys. Rev. B 77, 094416 (2008) · 24 pages, references added, the version which appears in the journal

openalex publication_date 2008/03/17 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck--Kennedy--Lieb--Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states of Hamiltonians with nearest-neighbor interactions.

Citations

• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• Antiferromagnetic model with known ground state
• Matrix product states represent ground states faithfully
• Two soluble models of an antiferromagnetic chain

Cited by

• Valence bond solid states with symplectic symmetry
• Exact models for trimerization and tetramerization in spin chains
• Homogeneous binary trees as ground states of quantum critical Hamiltonians
• Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states