Self-conjugate representation SU(3) chains

Abstract

It was recently argued that SU(3) chains in the $p$-box symmetric irreducible representation (irrep) exhibit a "Haldane gap" when $p$ is a multiple of 3 and are otherwise gapless [Nucl. Phys. B $924$, 508 (2017)]. We extend this argument to the self-conjugate irreps of SU(3) with $p$ columns of length 2 and $p$ columns of length 1 in the Young tableau ($p=1$ corresponding to the adjoint irrep), arguing that they are always gapped but have spontaneously broken parity symmetry for $p$ odd but not even.

15 pages + 6 pages of appendices, 4 figures

References in corpus (30)

• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• A one-dimensional liquid of fermions with tunable spin
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Spin-stretching modes in anisotropic magnets: spin-wave excitations in the multiferroic Ba2CoGe2O7
• Generalization of the Haldane conjecture to SU(3) chains
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• 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
• Coherent States For SU(3)
• Haldane limits via Lagrangian embeddings
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Multiboson spin-wave theory for Ba2CoGe2O7, a spin-3/2 easy-plane Neel antiferromagnet with strong single-ion anisotropy
• Sigma Models on Flags
• Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice
• A Note on (Spin-) Coherent-State Path Integral
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• A Strong-Coupling Analysis of the Lattice $C{P}^{N-1}$ Models in the Presence of a $\theta$ Term
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• The $\theta$-term, CP${}^{N-1}$ Model and the Inversion Approach in the Imaginary $\theta$ Method
• On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

Cited by in corpus (7)

• Generalization of the Haldane conjecture to SU($n$) chains
• Flag manifold sigma models: spin chains and integrable theories
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• Flag manifold sigma models from SU($n$) chains
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain
• Edge states and universality class of the critical two-box symmetric SU(3) chain
• Bosonic realization of SU(3) chiral Haldane phases