Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice

TL;DR

This study uses density matrix renormalization group methods to identify a spin liquid phase in the $S=1/2$ $J_1-J_2$ Heisenberg model on a triangular lattice, revealing a gapped, non-magnetic state between magnetic orders.

Contribution

It provides the first evidence of a gapped spin liquid phase in the $J_1-J_2$ Heisenberg model on the triangular lattice using large-scale DMRG simulations.

Findings

Evidence of a spin liquid phase at $J_2/J_1 \,\approx\, 0.1$

Detection of two quasi-degenerate ground states on even cylinders

Observation of a finite bulk energy gap and dimerization effects

Abstract

We study the $S=1/2$ Heisenberg model on the triangular lattice with nearest neighbor interaction $J_1$ and next nearest neighbor interaction $J_2$ with the density matrix renormalization group. We are able to study long open cylinders with widths up to 9 lattice spacings. At an intermediate $J_2$ region $0.06 \lesssim J_2/J_1 \lesssim 0.17$, we find evidence for a spin liquid (SL) state with short range spin-spin, bond-bond and chiral correlation lengths, bordered by a classical $120^\circ$ N\'eel ordered state at small $J_2$ and by a two sub-lattice collinear magnetically ordered state at larger $J_2$. Focusing on $J_2/J_1 = 0.1$, we find a number of signatures of a gapped SL phase: two quasi-degenerate ground states on even cylinders, with an energy gap that decreases exponentially with the cylinder width; a dimerization effect on odd cylinders; and large spin triplet and singlet bulk gaps.