BILAYERS OF CHIRAL SPIN STATES

We study the behavior of two planes of a quantum Heisenberg antiferrom agnet in the regime in which a chiral spin liquid is stabilized in eac h plane. The planes are coupled by an exchange interaction of strength J(3). We show that in the regime of small J(3) (for both ferromagneti c and antiferromagnetic coupling), the system dynamically selects an a ntiferromagnetic ordering of the ground state chiralities of the plane s. For the case of an antiferromagnetic interaction between the planes , we find that, at some critical value J(3)(c) of the interlayer coupl ing, there is a phase transition to a valence-bond state on the interl ayer links. We derive an effective Landau-Ginzburg theory for this pha se transition. It contains two U(1) gauge fields coupled to the order parameter field. We study the low-energy spectrum of each phase. Tn th e condensed phase an ''anti-Higgs-Anderson'' mechanism occurs. It effe ctively restores time-reversal invariance by rendering massless one of the gauge fields while the other held locks the chiral degrees of fre edom locally. There is no phase transition for ferromagnetic couplings .