A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain

Abstract

We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G${}_2$. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G${}_2$ analog of the famous AKLT chain.

In memory of Ian Affleck

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• On topological phases of spin chains
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Simplex solid states of SU(N) quantum antiferromagnets
• Entanglement in an SU(n) Valence-Bond-Solid State
• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
• Valence bond solid states with symplectic symmetry
• Matrix Product State Representations
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Entanglement in valence-bond-solid states on symmetric graphs
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Exploring Triality Explicitly: Convenient bases for $\mathrm{SO}(8)$, $\mathrm{Spin}(1,7)$, and ${\mathrm{G}}_2$