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arXiv:0906.3528 · Physical Review B

Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms

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

Published Jan 22, 2010• 42 citations
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Abstract

A Haldane conjecture is revealed for spin-singlet charge modes in $2N$-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 $N$ for attractive interactions at half-filling. The analog of the Haldane phase of the spin-1 Heisenberg chain is stabilized for $N=2$ 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-$N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.

DOI
10.1103/physrevb.81.020408

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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 the nature of the Mott-insulating phases of half-filled 2N2N2N-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 NNN. First, we single out charged, spin-singlet degrees of freedom that carry a pseudospin S=N/2\mathcal{S}=N/2S=N/2, making it possible to formulate a Haldane conjecture: For attractive interactions, we establish the emergence of Haldane insulating phases when NNN is even, whereas a metallic behavior is found when NNN is odd. We point out that the N=1,2N=1,2N=1,2 cases do not have the generic properties of each family. The metallic phase for NNN 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 NNN further depend on the parity of N/2N/2N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2N/2N/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)].
We investigate the ground-state properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the ppp-wave Kondo-Heisenberg lattice model) by means of the density-matrix renormalization-group method. The nonstandard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the ``ppp-wave'' spin density of conduction electrons, inducing a topologically nontrivial insulating ground state. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin profile in the ground state, we show that, at half filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end states. Beyond its intrinsic interest as a useful ``toy model'' to understand the effects of strong correlations on topological insulators, we show that the ppp-wave Kondo-Heisenberg model could be experimentally implemented in $p\text{\ensuremath{-}}\mathrm{band}$ optical lattices loaded with ultracold Fermi gases.
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 examine quantum phases emerging from the double degeneracy of ppp-orbital bands in attractive atomic Fermi gases loaded on a one-dimensional (1D) optical lattice. Our numerical simulations via the density-matrix renormalization group predict the emergence of a state with a charge excitation gap, namely the Haldane insulator phase. A mapping onto an effective spin-1 model reveals its physical origin. Moreover, we show that population imbalance leads to richer diversity of the quantum phases, including a phase-separated polarized state. Finally, we study the effects of the harmonic trap potential in this 1D chain.
We systematically investigate the stability of the symmetry-protected topological (SPT) Haldane phase in spin- 1 2 Heisenberg and half-filled Hubbard ladders coupled by ferromagnetic Hund's interactions. Using the density-matrix renormalization group method, we analyze key signatures of the Haldane phase: long-range string order, finite spin gap, and characteristic entanglement spectrum degeneracies. In spin-only Heisenberg ladders, we find immediate onset and continuous strengthening of the Haldane phase with increasing Hund's coupling. In contrast, the inclusion of charge fluctuations in Hubbard ladders leads to a nontrivial stability regime, revealing a robust yet bounded region where SPT order persists despite significant charge fluctuations. We identify distinct boundaries separating a trivial insulating phase from the Haldane SPT phase, governed by both Coulomb repulsion and Hund's coupling. Our results highlight the subtle interplay of spin and charge degrees of freedom in correlated itinerant systems and establish essential criteria for observing Haldane physics experimentally in fermionic ladder materials.
We show that ultracold two-component fermionic dipolar gases in an optical lattice with strong two-body on-site loss can be used to realize a tunable effective spin-one model. Fermion number conservation provides an unusual constraint that ${\ensuremath{\sum}}_{i}({S}_{i}^{z}){}^{2}$ is conserved, leading to a unique topological liquid phase in one dimension, which can be thought of as the gapless analog of the Haldane gapped phase of a spin-one Heisenberg chain. The properties of this phase are calculated numerically via the infinite time-evolving block decimation method and analytically via a mapping to a one-mode L\"uttinger liquid with hidden spin information.