NEW SOLUTIONS FOR THE ANISOTROPIC ANTIFERROMAGNETIC CHAIN

Abstract

Coherent states are proposed as solutions for the antiferromagnetic Heisenberg Hamiltonian in the quasi-Ising asymptotic regime of high anisotropy. Since our solutions are given in closed analytical form, a deep insight concerning the structure of the ground state and its excitations is obtained. Our calculation is in excellent agreement with numerical simulations. It has been suggested that the mechanisms involved in the recently discovered high-T, superconductivity are related to the magnetic properties of these new compounds [I]. This fact has drifted a special attention to the study of the antiferromagnetic properties of the insulating phase of these materials. As a prototype copper oxyde, La2Cu04-s appears as a likely candidate for a two-dimensional antiferromagnetic system, displaying also superconductivity for a given range of doping [2]. At this stage, a reliable description of the highly correlated insulating phase in these low dimensional materials is desirable. The above regime can be modelled by an antiferromagnetic Heisenberg Hamiltonian, which in spite of its deceivingly simple appearance, displays highly nontrivial many-body effects. The exact solution for the ground state in one-dimension, including anistropy, is available in the literature [3], but no exact solution is known for higher dimensions. Even in one-dimension, the solution obtained through the Bethe ansatz [3] is cumbersome and difficult to handle. Numerical results in higher dimensions are not conclusive and extrapolate differently [4]. In the present contribution we put forward a general 1 solution of the anisotropic spin-Heisenberg model 2 with antiferromagnetic coupling which is asymptotically exact in the high correlation limit. We illustrate this solution with the linear chain, where large size (N 20) numerical simulations and exact results are available for comparison. The Heisenberg Hamiltonian for the linear chain reads served in finite-size calculations for Heisenberg chains 151. As long as a remains smaller than 1, the ground state has a dominant component of the Ndel type. Next contributions come from configurations obtained from the NBel state by flipping one pair of spins, two pairs of them, and so on, in hierarchical order. Since the Ndel components dominate the overall quantum superposition, the ground state presents long-range order, but quantum fluctuations reduce considerably the staggered magnetization. This effect is similar to the one observed in LazCu04-6 by means of neutron diffraction experiments, where a reduction of the magnetic moment ascribed to C U + ~ ions is obtained [2]. The above considerations heuristically lead to the definition of the foilowing even and odd operators: + : = G c S+ (m + 1) S(m) + a f i , (2)