Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction

TL;DR

This study uses exact diagonalization to explore the phase diagram of the spin-1/2 triangular Heisenberg model with ring-exchange, revealing various magnetic and nonmagnetic phases but no evidence of a quantum spin liquid.

Contribution

First comprehensive exact diagonalization analysis of the triangular Heisenberg model with ring-exchange, identifying multiple phases and characterizing their properties.

Findings

Identification of magnetic ordered phases like zigzag and tetrahedral

Discovery of nonmagnetic valence bond solid phases

No evidence found for quantum spin liquid with spinon Fermi surface

Abstract

Using Lanczos exact diagonalization (ED), we study the spin-1/2 $J_1$-$J_2$ Heisenberg model with the four-spin ring-exchange interaction $J_r$ on triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer and chiral correlation functions. The ground state has rich phases including several magnetic ordered phases like zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction, and help to understand the relevant triangular materials.