Spin-1/2 quantum antiferromagnets on the triangular lattice

Abstract

The spin-2 anisotropic Heisenberg antiferromagnet is studied at T = 0 on the triangular lattice via numerical diagonalization for system sizes up to N = 36 sites. Extrapolation to the thermodynamic limit suggests that the isotropic system possesses no, or very small,~3 x~3 magnetic order; no helical or chiral order; and spin-spin correlations consistent with that of a critical phase. For A Y-like anisotropy there is long-ranged~3x~3 magnetic order. In contrast to bipartite lattices, the standard firstand second-order spin-wave theories are not quantitatively accurate. Excitation energy gaps suggest that the lowest-lying excitations for the isotropic point are not spin-Rip excitations in the thermodynamic limit. The results for the isotropic point appear to agree with recent series expansion, large-N expansion, and the original resonanting valence bond picture of Anderson, although they cannot be considered as conclusive evidence supporting any of these theories.

Long-Range Order of the Three-Sublattice Structure in the S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice

“…However, estimating the magnetic order of a three-sublattice structure (3SS) quantitatively by direct methods that are unbiased beyond any approximation or variational method is still difficult even now. Numerical diagonalization data of small finite-size (FS) clusters of up to 36 sites of the S ¼ 1=2 model [5][6][7] were examined. 8) However, Leung and Runge 7) and Bernu et al 6) reported the subtlety in quantitative extrapolation from their diagonalization data of spin correlation functions for observing the order directly.…”

Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

“…From the proposition of Anderson and Fazekas that this model is a candidate to exhibit spin liquid behavior 1 , a lot of work was done to understand the nature of its ground state. Although there is a general conviction that the ground state is ordered with a magnetic vector Q = (4π/3, 0) 2,3 , some authors found a situation very close to a critical one or no magnetic order at all, leaving the answer still controversial 4,5 . A systematic way to study the role of frustration is to vary the strength of the exchange interaction along the bonds.…”

Spin-liquid phase in an anisotropic triangular-lattice Heisenberg model: Exact diagonalization and density-matrix renormalization group calculations

“…1- 4 The isotropic spin-1 / 2 Heisenberg antiferromagnet ͑HAFM͒ on a triangular lattice was a candidate for the realization of a disordered spin-liquid phase, 1 but it turns out to exhibit a three-sublattice antiferromagneticlong-range-order ͑AFLRO͒ as established by analytic [5][6][7][8] and numerical 5,9,10 studies. Among various spin models, a spin-liquid phase has been established for more geometrically frustrated systems on the Kagome lattice, 11,12 dimer models, 13 and models involving four spin exchange terms.…”

“…The total number of sites is N = N 1 ϫ N 2 . The ground state is determined by a Lanczos diagonalization of the Hamiltonian using all symmetries 9,27 for system sizes up to N =36 ͑corresponding to a Hilbert space of a dimension N H = 630 928 37͒. On the other hand, the DMRG method 23,24 allows us to extend the exact calculation to larger systems up to N =8ϫ 18 sites ͑i.e., 8-legs͒.…”

“…This difference may be attributed to the importance of quantum fluctuations 21 in the model, which could have been underestimated in the linear SWT approach. We have carried out a standard SWT calculation by taking into account the magnon scattering and the geometrical frustration 7,9 up to the second order. Our result shows that the boundary of the disordered region indeed moves up to J c1 Ј = 0.39J from the linear SWT J c1 Ј = 0.27J.…”