SU(N) Heisenberg model with multi-column representations

The $\mathrm{SU}(N)$ symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the N\'eel order disappears at $N = 10$ indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the N\'eel and the valence-bond solid ordering for $N\ge 15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the N\'eel state, because the expected spontaneous order is too weak to be detected.Comment: 5 pages, 5 figure

Multiple-q states and skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields

Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both skyrmions and anti-skyrmions, together with a new thermodynamic phase where skyrmion and anti-skyrmion lattices form a domain state.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

Phase transition of the three-dimensional chiral Ginzburg-Landau model -- search for the chiral phase

Nature of the phase transition of regularly frustrated vector spin systems in three dimensions is investigated based on a Ginzburg-Landau-type effective Hamiltonian. On the basis of the variational analysis of this model, Onoda et al recently suggested the possible occurrence of a chiral phase, where the vector chirality exhibits a long-range order without the long-range order of the spin [Phys. Rev. Lett. 99, 027206 (2007)]. In the present paper, we elaborate their analysis by considering the possibility of a first-order transition which was not taken into account in their analysis. We find that the first-order transition indeed occurs within the variational approximation, which significantly reduces the stability range of the chiral phase, while the chiral phase still persists in a restricted parameter range. Then, we perform an extensive Monte Carlo simulation focusing on such a parameter range. Contrary to the variational result, however, we do not find any evidence of the chiral phase. The range of the chiral phase, if any, is estimated to be less than 0.1% in the temperature width.Comment: 19 pages, 17 figure