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arXiv:1107.0171 · Physical Review B

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

Heloise Nonne, P. Lecheminant, Sylvain Capponi, Guillaume Roux, E. Boulat

Published Sep 12, 2011• 35 citations
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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 pseudospin $\mathcal{S}=N/2$, making it possible 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 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 et al. [arXiv:0909.4059 (to be published)].

DOI
10.1103/physrevb.84.125123

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A Haldane conjecture is revealed for spin-singlet charge modes in 2N2N2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and density matrix renormalization group calculations, we show the emergence of gapless and gapped phases depending on the parity of NNN for attractive interactions at half-filling. The analog of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2N=2N=2 with nonlocal string charge correlation and pseudo-spin-1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin-N/2N/2N/2 operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.
We investigate possible realizations of exotic SU(N)\mathrm{SU}(N)SU(N) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even NNN, two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2N/2N/2 Haldane phase, and a topological SU(N)\mathrm{SU}(N)SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N)\mathrm{SU}(N)SU(N) topological phases found here.
We study various Mott insulating phases of interacting spin-32\frac{3}{2}23​ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.
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We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at halffilling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p -band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2 I + 1) symmetry which depend only on the nuclear-spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I (=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2 I + 1) symmetry.
The emergence of the Haldane Chern insulator state due to strong short-range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting (i) the absence of the Chern insulator state, (ii) two previously unnoticed charge ordered phases, and (iii) the existence and stability of all the nontopological competing orders that were found previously within mean field. In addition, we discuss the nature of the corresponding phase transitions based on our numerical data. Our work establishes the phase diagram of the half-filled honeycomb lattice model, tilting the balance towards the absence of a Chern insulator phase for this model.