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We study the phase diagram of the frustrated Heisenberg model on thetriangular lattice with nearest and next-nearest neighbor spin exchangecoupling, on 3-leg ladders. Using the density-matrix renormalization-groupmethod, we obtain the complete phase diagram of the model, which includesquasi-long-range $120^\circ$ and columnar order, and a Majumdar-Ghosh phasewith short-ranged correlations. All these phases are non-chiral and planar. Wealso identify the nature of phase transitions.

Phase Diagram of the Spin-$1/2$ Triangular $J_1$-$J_2$ Heisenberg Model on a 3-leg Cylinder