The matrix product representations for all valence bond states

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/VBS (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.

24 pages, references added, the version which appears in the journal

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Cited by in corpus (25)

• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• PEPS as ground states: degeneracy and topology
• Lecture Notes of Tensor Network Contractions
• Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Critical properties of homogeneous binary trees
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Valence bond solid states with symplectic symmetry
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Quantifying entanglement with scattering experiments
• Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Topological lattice field theories from intertwiner dynamics
• Dimerized ground states in spin-S frustrated systems
• Exact models for trimerization and tetramerization in spin chains
• The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
• Group-covariant extreme and quasi-extreme channels
• Entanglement of disjoint blocks in the one dimensional Spin 1 VBS
• Matrix Product State representation for Slater Determinants and Configuration Interaction States
• Exact symmetry breaking ground states for quantum spin chains
• Spin-spin correlation functions of the q-VBS state of an integer spin model
• Exact ground states for two new spin-1 quantum chains, new features of matrix product states
• A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices
• Pair entanglement in dimerized spin-s chains
• A new family of matrix product states with Dzyaloshinski-Moriya interactions