# Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet

## TL;DR

This study maps the phase diagram of a spin-1/2 triangular antiferromagnet, revealing magnetic orders and chiral spin liquids, with detailed analysis of phase transitions and topological properties using large-scale DMRG calculations.

## Contribution

It provides the first comprehensive phase diagram including scalar chiral interactions and identifies a chiral spin liquid as a fractional quantum Hall state.

## Key findings

- Identified a chiral spin liquid phase with fractional quantum Hall characteristics.
- Mapped magnetic and non-magnetic phases in the J1-J2-Jchi model.
- Found large spin triplet gap in odd sectors and small or vanishing gap in even sectors.

## 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 $J_{\chi}(\vec{S}_i \times \vec{S}_j) \cdot \vec{S}_k$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing $J_2$ ($J_2/J_1 \leq 0.3$) and $J_{\chi}$ ($J_{\chi}/J_1 \leq 1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered $120^{\circ}$ phase, stripe phase, and non-coplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $\nu = 1/2$ 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 $J_1 - J_2$ triangular model ($0.08 \lesssim J_2/J_1 \lesssim 0.15$) shows a phase transition to the CSL phase at very small $J_{\chi}$. We also compute spin triplet gap in both spin liquid phases, and our finite-size results suggest large gap in the odd topological sector but small or vanishing gap in the even sector. We discuss the implications of our results to the nature of the spin liquid phases.