One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

Abstract

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains (J J) and the isotropic triangular lattice (J = J). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at (J /J)c ∼ 0.42, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at (J /J)c ∼ 0.43. The agreement of these complementary methods, along with the strong difference found between the intra-and the interchain DMRG short spin-spin correlations; for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.

Stripe order and magnetic anisotropy in the S=1 antiferromagnet BaMoP2O8

“…The interlayer coupling J 3 is a more plausible candidate, because it is non-frustrated and couples the spin chains more efficiently. Our estimate of J 3 /J 2 0.043 is surprisingly close to the reported threshold value of J inter /J intra = 0.042 − 0.044 [59][60][61][62], although one should keep in mind that the interaction J 3 acts to induce the long-range order in the bc plane only, whereas the couplings in the ab plane remain frustrated. Finally, the single-ion anisotropy of A/J 2 0.06 is too weak to close the Haldane gap on its own, as higher values of A/J 2 ≥ 0.31 would be required in the absence of interchain couplings [63].…”

“…The S = 1 magnets should be less prone to the stripe order in the J 1 J 2 limit, because quantum fluctuations are reduced [58]. Moreover, decoupled chains form the Haldane phase protected by a spin gap, and a sizable J 1 /J 2 ≥ 0.3 = 0.4 [51,59] would be needed to induce the ordering. Since BaMoP 2 O 8 with its J 1 /J 2 0.1 is clearly below this threshold value, we conclude that J 1 can't cause long-range order in this system.…”

Gapped ground state in a spin-1/2 frustrated square lattice

“…As a result, a gapless disordered state analogous to a Tomonaga-Luttinger liquid (TLL) in a 1D system becomes stable in the spin-1/2 anisotropic triangular lattice, which is the so-called one-dimensionalization. For the spin-1 case, which corresponds to the mapped model in the present work, a dimensional reduction associated with the spatial anisotropy has also been suggested [16][17][18][19]. Cruciallly, unlike the gapless ground state in the spin-1/2 chain, a gapped Haldane state is formed in the spin-1 chain [20].…”

“…1(b). Theoretical studies on the spin-1 spatially anisotropic triangular indicate that one-dimensionalization caused by frustration can stabilize a Haldane state extended in a 2D system [16][17][18][19]. Although the present mapped triangular lattice differs in that the interchain couplings are F, such an extended Haldane state is expected to be stabilized.…”

Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions

“…On the other hand, phases with intact symmetry are better described by using the Schwinger bosonic representation [2][3][4][5], although three-dimensional models require special attention close to the transition temperature [6]. In general, the mean-field approach of the Schwinger formalism is sufficient for most of the scenarios; however, in frustrated models, the inclusion of Gaussian fluctuations should be considered [7][8][9][10], providing some extra complexity to the model. Moreover, it is also possible to represent the spin field by the non-linear sigma model O(3) [2,11,12] and then quantize the field fluctuations by standard techniques of quantum field theory (furthermore, note that in the AFM case, one should be careful with the topological phase).…”