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arXiv:1705.00510 · Physical review. B./Physical review. B

Global phase diagram and quantum spin liquids in a spin- 12 triangular antiferromagnet

Shou-Shu Gong, Wei Kang Zhu, Jian‐Xin Zhu, D. N. Sheng, Kun Yang

Published Aug 9, 2017• 107 citations
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Abstract

We study the spin-$1/2$ Heisenberg model on the triangular lattice with the nearest-neighbor ${J}_{1}>0$, the next-nearest-neighobr ${J}_{2}>0$ Heisenberg interactions, and the additional scalar chiral interaction ${J}_{\ensuremath{\chi}}({\stackrel{P\vec}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{P\vec}{S}}_{j})\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{P\vec}{S}}_{k}$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing ${J}_{2}$ (${J}_{2}/{J}_{1}\ensuremath{\le}0.3$) and ${J}_{\ensuremath{\chi}}$ (${J}_{\ensuremath{\chi}}/{J}_{1}\ensuremath{\le}1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered ${120}^{\ensuremath{\circ}}$, stripe, and noncoplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $\ensuremath{\nu}=1/2$ bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular model ($0.08\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.15$) shows a phase transition to the CSL phase at very small ${J}_{\ensuremath{\chi}}$. We also compute the spin triplet gap in both spin liquid phases, and our finite-size results suggest a large gap in the odd topological sector but a small or vanishing gap in the even sector. We discuss the implications of our results on the nature of the spin liquid phases.

DOI
10.1103/physrevb.96.075116

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