Phase Diagram of Spin-1/2 Triangular Antiferromagnet in a Magnetic Field

We investigate the spin-1/2 quantum Heisenberg antiferromagnet on both two-dimensional triangular lattice and N-leg triangular ladder. The model describes isotropic Heisenberg chains (exchange constant $J$) coupled antiferromagnetically through interchain diagonal bonds (exchange constant $J$'). We study different regions using various controlled theoretical methods. Primarily we focus on the region slightly below saturation field. We show that the cone-coplanar state transition is absent, while commensurate-incommensurate transition emerges right below the saturation field for two-dimensional triangular lattice. We also determine the ground states in the limit $J'\ll J$, using one-dimensional bosonization, renormalization group methods and current algebra. Finally, we compare our theoretical result with DMRG result for N-leg ladder.