"Haldane" phases with ultracold fermionic atoms in double-well optical lattices

Abstract

We propose to realize one-dimensional topological phases protected by SU($N$) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of $N$, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters of the model. For even $N$, the celebrated spin-1 Haldane phase and its generalization to SU($N$) are obtained with no local symmetry breaking. In stark contrast, at least for $N=3$, a new class of SPT phases, dubbed chiral Haldane phases, that spontaneously break inversion symmetry, emerge with a two-fold ground-state degeneracy. The latter ground states with open-boundary conditions are characterized by different left and right boundary spins which are related by conjugation. Our results show that topological phases are within close reach of the latest experiments on cold fermions in optical lattices.

4 pages main article (4 figs.), 1 page acknowledgement and bibliography, 9 pages Supp. Mat. (8 figs.)

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Cited by in corpus (11)

• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• 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
• 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
• Ground State Phase Diagram of $\text{SU}(3)$ $t$-$J$ Chain
• Bosonic realization of SU(3) chiral Haldane phases