Quantum phase transitions in the triangular-lattice bilayer Heisenberg model

We study the triangular-lattice bilayer Heisenberg model with antiferromagnetic interplane coupling J(perpendicular to) and nearest-neighbor intraplane coupling J = lambda J(perpendicular to) by expansions in lambda. For negative lambda a phase transition is found to an ordered phase at a lambda(c) = -0.3636 +/- 0.0001, which is in the 3D classical Heisenberg universality class. For lambda > 0, we find a transition at a rather large lambda(c) approximate to 1.2. The universality class of the transition is consistent with that of Kawamura's 3D antiferromagnetic stacked triangular lattice. The spectral weight for the triplet excitations, at the ordering wave vector, remains finite at the transition, suggesting that a phase with free spinons does not exist in this model. [S0031-9007(98)07709-6].