Erratum: Quantum Phase Diagram of the Triangular-LatticeXXZModel in a Magnetic Field [Phys. Rev. Lett. 112, 127203 (2014)]

Abstract

We have realized that the transition between the up-up-down and 0-coplanar states near the Ising limit is actually of the first order, although the hysteresis region is very narrow. In Fig. 1(a), we present the corrected quantum phase diagram, in which the boundary of the corresponding transition for 0 < J=J z < 0.437 is replaced by a thick blue line. This minor correction does not affect the rest of the phase diagram and the main conclusions of our Letter, including the novel degeneracy-lifting mechanism that gives rise to the new π-coplanar state.A recent theoretical work based on the density matrix renormalization group method has suggested the existence of the first-order transition for 0 < J=J z ≲ 0.4 [3]. Therefore, we reexamined the magnetization curve m z ðHÞ ¼ P i hŜ z i i=M for small positive values of the anisotropy J=J z . As shown in Fig. 1(b), the magnetization curve is three valued in a finite range of H=J z near the end point of the plateau (H ¼ H c2 ), which implies that the transition is of the first order. When J=J z increases, the sign of the susceptibility χ c2 ≡ dm z =dHj H¼H c2 just above the plateau changes from negative to positive; i.e., there is a tricritical point (TCP) where the transition nature changes from first order to second order. In Fig. 1(c), we show the extrapolation of the inverse of χ c2 with respect to the scaling parameter λ for different values of J=J z . The location of the TCP is estimated to be ðJ=J z Þ TCP ≈ 0.437, for which the extrapolated value of χ −1 c2 is 0. This result is consistent with Ref.[3].[1] S. Wessel and M. Troyer, Phys. Rev. Lett. 95, 127205 (2005).[2] L. Bonnes and S. Wessel, Phys. Rev. B 84, 054510 (2011).[3] D. Sellmann, X.-F. Zhang, and S. Eggert, arXiv:1403.0008.FIG . 1 (color online). (a) Ground-state phase diagram of the spin-1=2 triangular-lattice XXZ model obtained by the cluster mean-field method combined with a scaling scheme (CMF þ S) (J z > 0). The thick blue (thin black) solid curves correspond to first-(second-)order transitions. The dot marks the tricritical point. The latest quantum Monte Carlo data [1,2] are shown by the red dashed (first-order) and dotted (second-order) curves. The symbol (×) is the value from the dilute Bose gas expansion. (b) An example of the magnetization curve that exhibits a first-order transition. We show the magnetization m z divided by the saturation value S ¼ 1=2 as a function of the magnetic field H=J z . The vertical dashed line marks the first-order transition point. (c) Cluster-size scalings of the CMF data for the inverse susceptibility χ −1 c2 just above the plateau. The lines indicate linear fits to the data obtained from the three largest clusters for each J=J z .

Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation

“…has recently received increasing attention since the latest theoretical studies [29,30] indicated the possibility for the emergence of a new magnetic phase, named the π-coplanar or Ψ phase for J > J z > 0.…”

“…1). Whereas the former two already exist in the classical counterpart of the model [31], the latter emerges due to quantum-mechanical effects [29]. …”

“…[34], some of the current authors calculated a quantitatively precise result for the coplanar-umbrella transition point at H = H s − 0 + for arbitrary S, by treating the 1/S series exactly within the dilute Bose-gas framework [35]. This approach, however, makes it technically difficult to address the distinction [29,30] in the vicinity of the saturation field Hs = 3(J + 2Jz)S.…”

Static and Dynamical Properties of the Spin-1/2Equilateral Triangular-Lattice AntiferromagnetBa3CoSbMa1, Kamiya2, Hong3 et al. 2016Phys. Rev. Lett.135201454View full textAdd to dashboardCite

“…Introduction.-The S = 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) is the paradigmatic example of a two-dimensional (2D) frustrated quantum magnet [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The combination of frustration, strong quantum fluctuations and low dimensionality is anticipated to produce strong deviations from semiclassical theories.…”

“…• structure were compared as the "ab" and "ac" plane models, which are favored by easy-plane and easy-axis anisotropy, respectively [11,12,33]. The ab plane model corresponds to a 120…”