Schwinger boson mean field study of the $J_1$-$J_2$ Heisenberg quantum antiferromagnet on the triangular lattice

Abstract

We use Schwinger boson mean field theory (SBMFT) to study the ground state of the spin-$S$ triangular-lattice Heisenberg model with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic interactions. Previous work on the $S=1/2$ model leads us to consider two spin liquid Ansätze, one symmetric and one nematic, which upon spinon condensation give magnetically ordered states with 120${}^{\circ }$ order and collinear stripe order, respectively. The SBMFT contains the parameter $\kappa$, the expectation value of the number of bosons per site, which in the exact theory equals $2S$. For $\kappa =1$ there is a direct, first-order transition between the ordered states as $J_2/J_1$ increases. Motivated by arguments that in SBMFT, smaller $\kappa$ may be more appropriate for describing the $S=1/2$ case qualitatively, we find that in a $\kappa$ window around 0.6, a region with the (gapped $Z_2$) symmetric spin liquid opens up between the ordered states. As a consequence, the static structure factor has the same peak locations in the spin liquid as in the 120${}^{\circ }$ ordered state, and the phase transitions into the 120${}^{\circ }$ and collinear stripe ordered states are continuous and first-order, respectively.

11 pages, 7 figures, 2 tables

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