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

TL;DR

This paper maps out the phase diagram of a frustrated spin-1/2 triangular Heisenberg model on a 3-leg ladder, revealing various ordered phases and phase transitions using DMRG.

Contribution

It provides the first complete phase diagram of the model on a 3-leg ladder, identifying multiple phases and their transition characteristics.

Findings

Identification of quasi-long-range 120° and columnar order phases

Discovery of a Majumdar-Ghosh phase with short-range correlations

Characterization of phase transition types

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.