Triangular $J_1$-$J_2$ Heisenberg Antiferromagnet in a Magnetic Field

TL;DR

This study maps the phase diagram of the $J_1$-$J_2$ triangular Heisenberg antiferromagnet in a magnetic field, revealing field-induced magnetic orders, magnetization plateaux, and quantum spin-liquid phases through multiple computational methods.

Contribution

It provides a comprehensive analysis of the phase diagram using three approaches, clarifying the competition among magnetic orders and identifying quantum spin-liquid behavior in specific parameter regimes.

Findings

Identification of magnetization plateaux at 1/3 and 1/2 magnetization levels.

Discovery of a quantum spin-liquid phase with monopoles near $J_2/J_1=1/8$.

Resolution of competing magnetic orders in the phase diagram.

Abstract

The behavior of the paradigmatic $J_1-J_2$ triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaux across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around $J_2/J_1=\frac{1}{8}$ in which i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and ii) by further increasing the field, two plateaux are clearly obtained at $m=\frac{1}{3}$ and $m=\frac{1}{2}$. We discuss the experimental importance of the consecutive magnetization plateaux transitions as a signature of an underlying quantum spin-liquid phase.