Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture

Abstract

We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin $\mathcal{S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd. We point out that the $N=1,2$ cases do \emph{not} have the generic properties of each family. The metallic phase for $N$ odd and larger than 1 has a quasi-long range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even $N$ further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann {\it et al.} [Pollmann {\it et al.}, arXiv:0909.4059 (2009)].

25 pages, 20 figures

References in corpus (21)

• Bosonizing one-dimensional cold atomic gases
• Hidden order in 1D Bose insulators
• Implementation of Spin Hamiltonians in Optical Lattices
• Rise and fall of hidden string order of lattice bosons
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
• Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap
• On $c=1$ critical phases in anisotropic spin-1 chains
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• SU(N) quantum spin models: A variational wavefunction study
• Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies
• Homogeneous and inhomogeneous magnetic phases of constrained dipolar bosons
• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Current Carrying Ground State in a Bi-layer Model
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Competing orders in the generalized Hund chain model at half-filling
• Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension
• Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory
• Low-energy Effective Theory for One-dimensional Lattice Bosons near Integer Filling
• Quantum Phase Transitions and the Hidden Order in a Two-Chain Extended Boson Hubbard Model at Half-Odd-Integer Fillings

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