Exact diagonalization study of the anisotropic Heisenberg model related to YbMgGaO\(_4\) and NaYbCh\(_2\)

Abstract

Employing high-precision exact diagonalization, we systematically study the anisotropic Heisenberg model which is related to rare-earth triangular-lattice materials. From the finite-size low-energy spectra and the finite-size scaling of magnetic orders, we probe the full 3D phase diagram and identify all the phases. Remarkably, we find a large region of quantum spin liquid phase in the model with nearest-neighbor anisotropic exchange interactions. After adding the next-nearest-neighbor interaction, that phase can adiabatically connect to quantum spin liquid phase in the \(J_1-J_2\) triangular Heisenberg model. We also explore the magnetization curves of different phases and reproduce the remnant of 1/3-magnetization plateau in the quantum spin liquid phase. In addition, to study the possible chemical disorders in real materials, we consider the randomness of exchange interactions and find no spin glass order even in the strongest bond randomness case. All of our ED calculations give detailed insightful understanding of the microscopic Hamiltonian related to the YbMgGaO\(_4\), NaYbCh\(_2\) and some other related rare-earth triangular-lattice materials.