# Ground-state phase diagram of an anisotropic spin-$1/2$ model on the triangular lattice

## TL;DR

This study maps the ground-state phase diagram of an anisotropic spin-1/2 model on a triangular lattice, revealing multiple phases and phase transitions, but no evidence of a quantum spin liquid, thus informing the modeling of YbMgGaO4.

## Contribution

The paper provides a detailed phase diagram of the anisotropic spin-1/2 model using advanced numerical methods, highlighting the nature of phase transitions and the absence of a quantum spin liquid in this model.

## Key findings

- Identifies a 120° phase and two stripe phases in the quantum phase diagram.
- First-order transitions from stripe phases to the 120° phase.
- No evidence of a quantum spin liquid in the studied model.

## Abstract

Motivated by the recent experiment on a rare-earth material YbMgGaO$_4$ [Y. Li \textit{et al.}, Phys. Rev. Lett. \textbf{115}, 167203 (2015)], which found that the ground state of YbMgGaO$_4$ is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-$1/2$ model that was proposed to describe YbMgGaO$_4$. Using the density-matrix renormalization group method in combination with the exact diagonalization, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram there is a $120^{\circ}$ phase and two distinct stripe phases. The transitions from the two stripe phases to the $120^{\circ}$ phase are of the first order. However, the transition between the two stripe phases is not the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may be also important to model the material YbMgGaO$_4$. These findings will stimulate further experimental and theoretical works in understanding the quantum spin liquid ground state in YbMgGaO$_4$.