Ground-State Properties and Phase Diagram of the QuantumXXZAntiferromagnet on a Triangular Lattice

Long-range order, especially chiral order, in the two-dimensional spin \(1/2 XXZ\) antiferromagnet H = J ∑( S i x S j x + S i y S j y +Δ S i z S j z ) on a triangular lattice is studied, partially by showing exact ground states and partially using the spin-wave theory. Exact ground states in the region Δ≤-0.5 are found. These states are not disordered by quantum fluctuation. Most of the ground states at Δ=-0.5 have a so-called 120° structure. Ground-state properties in the region -0.5≤Δ≤1 are studied using the spin-wave theory. It is shown that quantum fluctuations are enhanced in the ground states as Δ is increased. The phase diagram of the relevant system at low temperatures is also discussed using the spin-wave theory.