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

Abstract

We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest and next-nearest neighbor spin exchange coupling, on 3-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range $120^{\circ }$ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are non-chiral and planar. We also identify the nature of phase transitions.

12 pages, 15 figures, 1 table, and no supplemental materials. v3: equivalent to the published version

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