The Haldane gap in the SU(3) [3 0 0] Heisenberg chain

Abstract

We calculate the Haldane gap of the $\mathrm{SU}(3)$ spin $[300]$ Heisenberg model using variational uniform fully symmetric $\mathrm{SU}(3)$ matrix product states, and find that the minimal gap $\Delta /J=0.0263$ is obtained in the $[210]$ sector at momentum $2\pi /3$. We also discuss the symmetry protected topological order of the ground state, and determine the full dispersion relation of the elementary excitations and the correlation lengths of the system.

References in corpus (13)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Transfer Matrices and Excitations with Matrix Product States
• On topological phases of spin chains
• Riemannian optimization of isometric tensor networks
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Generalization of the Haldane conjecture to SU($n$) chains
• Flag manifold sigma models: spin chains and integrable theories
• Spinon confinement and deconfinement in spin-1 chains
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Cited by in corpus (3)

• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Bosonic realization of SU(3) chiral Haldane phases