Bosonic realization of SU(3) chiral Haldane phases

Abstract

We give a bosonic realization of the SU(3) antiferromagnetic Heisenberg (AFH) chain in the alternating conjugate representation, and study its phase diagram as a function of staggered interactions and anisotropy along the $T^3$ and $T^8$ directions. Unlike the SU(2) case, we observe a chiral-reversed quantum phase transition, where each competing phase is adiabatically connected to one of the chiral Haldane phases predicted in the SU(3) AFH chain with local adjoint representation. In the vicinity of the Heisenberg point, we identify a symmetry-protected topological state that appears at the first excited energy level. We also study the spontaneous ${\mathbb{Z}}_3$ symmetry breaking of the system, and provide a variational wavefunction that captures the transition from the topological phase to the trivial phase. Finally, we propose an experimental realization of our bosonic model by two spin-1/2 bosons in an optical lattice.

16 pages, 25 figures

References in corpus (22)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• The ALPS project release 1.3: open source software for strongly correlated systems
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Matrix Product State applications for the ALPS project
• On topological phases of spin chains
• 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
• Spin-1 bosons with coupled ground states in optical lattices
• Photoassociation spectroscopy of a Spin-1 Bose-Einstein condensate
• Spectral and Entanglement Properties of the Bosonic Haldane Insulator
• Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Coherent heteronuclear spin dynamics in an ultracold spin-1 mixture
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Two-photon photoassociation spectroscopy of an ultracold heteronuclear molecule
• Phase diagram of spin-1/2 bosons in one-dimensional optical lattice
• Coupled two-component atomic gas in an optical lattice
• Manipulation of heteronuclear spin dynamics with microwave and vector light shift
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain
• Experimental realization of a SU(3) color-orbit coupling in an ultracold gas