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arXiv:1201.0722 · Chinese Physics Letters

Nematic Ferromagnetism on the Lieb Lattice

Ke-Ji Chen, Wei Zhang

Published Nov 1, 2014• 5 citations
arXivHTMLPDF

Abstract

We discuss the properties of ferromagnetic orders on the Lieb lattice and show that a symmetry protected quadratic-flat band crossing point will dramatically affect the magnetic ordering. In the presence of a weak on-site repulsive interaction, the ground state is a nematic ferromagnetic order with simultaneously broken time-reversal and rotational symmetries. When the interaction strength increases, the rotational symmetry will restore at a critical value, and the system enters a conventional ferromagnetic regime. The mean-field transition temperatures for both the nematic and conventional ferromagnetic phases are in the order of interaction. This observation suggests that these magnetic orders have the potential to be realized and detected in cold atomic systems within realistic experimental conditions.

DOI
10.1088/0256-307x/31/11/110303

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The ground state phase diagram of a general isotropic spin-3/2 system with nearest-neighbor exchange is shown to contain unconventionally ordered spin nematic and antinematic states, as well as usual ferro- and antiferromagnetic phases. The two nematic phases have spontaneously broken rotational symmetry characterized by the long-range order of the nematic director u, as well as the broken time-reversal symmetry described by the pseudospin vector σ. Nematic phase differs from antinematic one by the type of ordering in σ vectors (uniform versus staggered). The ferromagnet-nematic and antiferromagnet-antinematic phase boundaries exhibit enhanced Sp(4) symmetry and correspond to the recently studied effective theory for spin-3/2 cold gases. We discuss optical properties and topological defects in the nematic phases.
We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator. The latter phase breaks the rotational, but not the time-reversal, symmetry and may be relevant to materials such as gray tin or mercury telluride at low temperatures. The critical point represents a simple quantum analog of the familiar classical isotropic-to-nematic transition in liquid crystals. The properties and the consequences of this quantum critical point are discussed. Its existence supports the scenario of the ``fixed-point collision,'' according to which three-dimensional Fermi systems with quadratic band touching and long-range Coulomb interactions are unstable towards the gapped nematic ground state at low temperatures.
The higher-spin Kitaev magnets, in which the Kitaev interaction and off-diagonal exchange couplings are overwhelmingly large, have emerged as a fertile avenue to explore exotic phases and unusual excitations. In this paper, we study the quantum phase diagram of the spin-1 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice using density-matrix renormalization group. It harbors six distinct phases and the intriguing findings are three magnetically ordered phases in which both time-reversal symmetry and lattice symmetry, albeit of different sorts, are broken spontaneously. The chiral spin state originates from the order-by-disorder effect and exhibits an almost saturated scalar spin chirality at the quantum level. Depending on the relative strength of the two interactions, it also features a columnarlike or plaquettelike dimer pattern as a consequence of the translational symmetry breaking. In parallel, the nematic ferromagnets are situated at the ferromagnetic Kitaev side and possess small but finite ferromagnetic ordering. The lattice-rotational symmetry breaking enforces nonequivalent bond energy along one of the three bonds. Although the intrinsic difference between the two nematic ferromagnets remains elusive, the discontinuities in the von Neumann entropy, hexagonal plaquette operator, and Wilson loop operator convincingly suggest that they are separated via a first-order phase transition.
We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux +/-2pi if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.
We investigate the magnetic properties of a repulsive fermionic SU(3)\mathrm{SU}(3)SU(3) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the SU(2\mathrm{SU}(2SU(2) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of SU(3)\mathrm{SU}(3)SU(3) symmetry. We find that, at 4/94/94/9 filling, the SU(3)\mathrm{SU}(3)SU(3) symmetry spontaneously breaks into the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive UUU at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from 4/94/94/9, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than what can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.