科研之友
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摘要
We use projector quantum Monte Carlo methods to study the doublet ground states of two-dimensional S = 1/2 antiferromagnets on L x L square lattices with L odd. We compute the ground-state spin texture Phi(z)((r) over bar) = %26lt; S-z((r) over bar)%26gt;up arrow in the ground state vertical bar G %26gt;up arrow with S-tot(z) = 1/2, and relate n(z), the thermodynamic limit of the staggered component of Phi(z)((r) over bar), to m, the thermodynamic limit of the magnitude of the staggered magnetization vector in the singlet ground state of the same system with L even. If the direction of the staggered magnetization in vertical bar G %26gt;up arrow were fully pinned along the (z) over cap axis in the thermodynamic limit, then we would expect n(z)/m = 1. By studying several different deformations of the square lattice Heisenberg antiferromagnet, we find instead that n(z)/m is a universal function of m, independent of the microscopic details of the Hamiltonian, and well approximated by n(z)/m approximate to 0.266 + 0.288m - 0.306m(2) for S = 1/2 antiferromagnets. We define n(z) and m analogously for spin-S antiferromagnets, and explore this universal relationship using spin-wave theory, a simple mean-field theory written in terms of the total spin of each sublattice, and a rotor model for the dynamics of the staggered magnetization vector. We find that spin-wave theory predicts n(z)/m approximate to (0.987 - 1.003/S) + 0.013m/S to leading order in 1/S, while the sublattice-spin mean-field theory and the rotor model both give n(z)/m = S/(S + 1) for spin-S antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range unfrustrated exchange interactions.
- 出版日期2012-8-13
