Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation

Abstract

Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications for a potential multicritical nature of topological phase transitions.

19 pages, 3 tables, lots of figures

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Cited by in corpus (23)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Generalization of the Haldane conjecture to SU(3) chains
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Mixed global anomalies and boundary conformal field theories
• Flag manifold sigma models: spin chains and integrable theories
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Quantum many-body spin ratchets
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Image-processing the topological charge density in the CP(N-1) model
• Edge mode locality in perturbed symmetry protected topological order
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Nonabelian ferromagnets with three-body interactions
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• 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
• Interrelations among frustration-free models via Witten's conjugation
• Adjoint ferromagnets
• Bosonic realization of SU(3) chiral Haldane phases