Quantum phase transitions in triangular lattice Heisenberg anti-ferromagnet in a magnetic field

We present the zero temperature phase diagram of a large $S$ Heisenberg anti-ferromagnet on a frustrated triangular lattice with the nearest neighbor ($J_1$) and the next nearest neighbor ($J_2$) interactions, in a magnetic field. We show that the classical model has an “accidental” degeneracy for all $J_2/J_1$ and all fields below the saturation field, which gives rise to the extended manifold of the ground state spin configurations. Quantum fluctuations, however, lift this degeneracy. For small $J_2/J_1$, they select one of three different co-planar states, depending on the field value. We argue that above some critical ratio of $J_2/J_1$, which weakly depends on a magnetic field, these fluctuations select the stripe phase. We analyze in detail the mechanism of the selection of the stripe phase and explore the nature of the quantum phase transition in a magnetic field between the ordered phases as $J_2/J_1$ passes through a critical value.