Erratum: Quadrupolar Phases of theS=1Bilinear-Biquadratic Heisenberg Model on the Triangular Lattice [Phys. Rev. Lett.97, 087205 (2006)]

Abstract

Below Eq. (2) in Ref. [1], there is a misprint in the formula relating the scalar product of spin and quadrupolar operators to the permutation operator. The sign in front of the permutation is wrong, and the correct formula readsAs it is written in the Letter, Eq. (5) is valid for pure quadrupolar states (real d 0 s), but not for the general case of complex d 0 s. The correct form of Eq. (5) for the general case readsThis does not affect any of the results reported in the Letter. We have only used this equation to discuss the relationship between the sign of the biquadratic coupling and the type of quadrupolar order (ferroquadrupolar versus antiferroquadrupolar). The determination of the phase diagram has been performed using a different parametrization.

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadraticS=1Heisenberg chain in a magnetic field

“…Note that the directors are perpendicular to the field. In previous work, ferroquadrupolar long-range-order has been identified for the S = 1 bilinear-biquadratic Heisenberg model on the square 35 and triangular lattice 4 at zero magnetic field. In the 1D case, at zero field spin-nematic phases have been identified numerically.…”

“…2: on a single site, a finite expectation value Q i can be envisaged as fluctuations around an axis called director. 4 In a ferroquadrupolar phase, all directors align parallel to each other. Note that the directors are perpendicular to the field.…”

“…1,2 Recent findings on NiGa 2 S 4 , a spin-1 material on a triangular lattice, 3 indicate the possible realization of such a spin-nematic phase. Theoretical investigations of the bilinearbiquadratic S = 1 Heisenberg model on this lattice geometry have shown that it is possible to stabilize spin-nematic LRO of ferroquadrupolar and antiferroquadrupolar type depending on the sign of the biquadratic interaction, 4,5 and that applying an external magnetic field leads to a remarkably rich phase diagram, with in particular a 2/3 magnetization plateau above the antiferroquadrupolar phase. 4 In this paper we investigate the one-dimensional version of the model defined by the Hamiltonian…”

Ground-state properties of antiferromagnetic anisotropicS=1Heisenberg spin chains

“…At sufficiently small negative values of D, one observes the (IC) 1 region. This region may be subdivided into two parts: At larger magnetizations, we observe ferroquadrupolar ordering, [25][26][27] where the algebraic decay of the four-point transverse cor- relation function (S + i ) 2 (S − i+r ) 2 is slower than that of z (r), due to a smaller exponent η. At lower magnetizations, one encounters a spin-density-wave ordering, with the longitudinal spin correlations being dominant.…”

Fermionic theory for quantum antiferromagnets with spinS>12

“…The system has a CurieWeiss temperature ϳ80 K, and is found to exhibit no conventional magnetic order down to 0.35 K. Several plausible ground states have been proposed for this system, [22][23][24][25][26][27][28] including an antiferronematic state, 24 a ferronematic state, 23 and a KT phase driven by vortices. 28 Spin liquid is also proposed to be a plausible ground state.…”