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arXiv:1103.1926 · Physical Review B

Quantum magnetism in ultracold alkali and alkaline-earth fermion systems with symplectic symmetry

Hsiang-Hsuan Hung, Yupeng Wang, Congjun Wu

Published Aug 2, 2011• 37 citations
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Abstract

We numerically study the quantum magnetism of ultracold alkali and alkaline-earth fermion systems with large hyperfine spin $F=\frac{3}{2}$, which are characterized by a generic $Sp(N)$ symmetry with $N=4$. The methods of exact diagonalization (ED) and density matrix renormalization group are employed for the large size one-dimensional (1D) systems, and the ED method is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges ${J}_{0}$ and ${J}_{2}$ in the bond spin singlet and quintet channels, respectively. In one dimension, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at ${J}_{0}/{J}_{2}>1$ and a gapless spin-liquid state at ${J}_{0}/{J}_{2}\ensuremath{\leqslant}1$, respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In two-dimensions, various spin-correlation functions are calculated up to the size of $4\ifmmode\times\else\texttimes\fi{}4$. The N\'eel-type spin correlation dominates at large values of ${J}_{0}/{J}_{2}$, while a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competition among the plaquette ordering, the dimer ordering, and the N\'eel ordering in the 2D system.

DOI
10.1103/physrevb.84.054406

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The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.
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