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Abstract

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin-lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. The ground-state energy and the sublattice magnetization are calculated for the square-lattice and triangular-lattice Heisenberg antiferromagnets, and our best estimates give values for the sublattice magnetization which are 62% and 51 % of the classical results for the square and triangular lattices, respectively. We furthermore make a conjecture as to why previous series expansion calculations have not indicated Neel-like long-range order for the triangular-lattice Heisenberg antiferromagnet. We investigate the critical behavior of the anisotropic systems by obtaining approximate values for the positions of phase transition points.

Coupled cluster treatment of an interpolating triangle-kagoméantiferromagnet

“…Our approach is now to "track" this solution for decreasing values of J ′ until we reach a critical value of J ′ c at which the solution to the CCM equations breaks down. This is associated with a phase transition in the real system [10], and results for J ′ c for this model are presented in Table I. A simple "heuristic" extrapolation of these results gives a value of J ′ c = 0.0 ± 0.1 for the position of this phase transition point.…”

“…1). By contrast, previous calculations [10] for the TAF used a unit cell containing only a single site per unit cell. Hence, the J-J ′ model has many more "fundamental" configurations than the TAF model at equivalent levels of approximation.…”

“…We now briefly describe the general CCM formalism, although for further details the interested reader is referred to Refs. [10,15]. The exact ket and bra groundstate energy eigenvectors, |Ψ and Ψ |, of a general manybody system described by a Hamiltonian H,…”

“…The fixed-node quantum Monte Carlo (FNQMC) method [6] has however been applied to this system with some success, although the results constitute only a variational upper bound for the energy. Other approximate methods [7,8,9,10] have also been successfully applied to the spin-half TAF, and most, but not all, such treatments predict that about 50% of the classical Néel-like ordering on the three equivalent sublattices remains in the quantum case. In particular, series expansion results [7] give a value for the groundstate energy of E g /N =−0.551, although the corresponding value for the amount of remaining classical order of about 20% is almost certainly too low.…”

“…The interested reader is referred to Ref. [10] for a full account of how such highorder CCM techniques are applied to lattice quantum spin systems. We note that for the CCM treatment of the J-J ′ model presented here the unit cell contains four lattice sites (see Fig.…”