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Register a new userSpin-Wave Theory for the Scalar Chiral Phase in the Multiple-Spin Exchange Model on a Triangular Lattice
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We study the effects of quantum fluctuations on a non-coplanar tetrahedral spin structure, which has a scalar chiral order, in the spin-1/2 multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice. We find that, in the linear spin-wave approximation, the tetrahedral structure survives the quantum fluctuations because spin waves do not soften in the whole parameter region of the tetrahedral-structure phase evaluated for the classical system. In the quantum corrections to the ground-state energy, sublattice magnetization, and scalar chirality, the effects of the quantum fluctuations are small for the ferromagnetic nearest-neighbor interactions and for the strong five-spin interactions. The six-spin interactions have little effect on the quantum corrections in the tetrahedral-structure phase. This calculation also corrects an error in the previously reported value of scalar chirality for the spin-1/2 multiple-spin exchange model with up to the four-spin exchange interactions.
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By combining the density matrix renormalization group (DMRG) method with Gutzwiller projected wave functions, we provide clear evidence that the ground state of the SU(4) Kugel-Khomskii spin-orbital model on the triangular lattice can be well described by a ``single Gutzwiller projected wave function with an emergent parton Fermi surface, despite it exhibits strong finite size effect and even-odd discrepancy in quasi-one-dimensional cylinders. This ground state preserves SU(4) symmetry, but spontaneously breaks translational symmetry by doubling the unit cell along one of the lattice vector directions. The finite size effect and even-odd discrepancy can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space. Thereby, a nematic spin-orbital liquid state is expected in the two-dimensional limit. Furthermore, our DMRG results indicate that the fluctuating stripes are critical and the central charge of each stripe is $c=3$, in agreement with the SU(4)$_1$ Wess-Zumino-Witten conformal field theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.
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The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard (TLU) model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{rm{spin}} otimes $U(1)$_{rm{charge}}$ symmetries implemented, we study the TLU model defined on the long cylinder geometry with circumference $W=4$. A gapped quantum spin liquid, with on-site interaction $9 lesssim U / t lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the large degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.
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