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

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.

Figures (5)

• Figure 1: Top: Phase diagram of the $J_1-J_2-H$ model determined from self-consistent NLSWT on a $30\times 30$ triangular lattice with PBC. Dotted lines indicate classical phase boundaries between three- and four-sublattice and fully polarized phases. Solid (dashed) lines indicate first (second) order phase transitions. The light gray area denotes the expected breakdown of semiclassical configurations as predicted from LSWT and mode condensation. The $m=\frac{1}{3}$ (UUD) and $m=\frac{1}{2}$ (UUUD) magnetization plateaux are highlighted in light blue and green, with their phase boundaries highlighted in yellow. The purple box contains a region beyond the reach of the semiclassical theory. Bottom: The low-field phase diagram of the $J_1-J_2-H$ model in the vicinity of QSL obtained from VMC on an $18 \times 18$ triangular lattice.
• Figure 2: Magnetization cuts marked by the blue arrowheads on the axes of Fig. \ref{['fig:phasediag']}(top), obtained from different methods; phases are colored according to the results from self-consistent stable ($m_{SW,S}$) and local NLSWT ($m_{SW,S}$). The crosses are obtained from the local algorithm, the continuous line from the stable algorithm and the DMRG data obtained on a $6\times 24$ cylinder is shown using circles. Both NLSWT algorithms run on a $30\times 30$ lattice using PBC. The dashed line shows the classical magnetization. (a, b) Plots as a function of $H/J_1$ at fixed $J_2/J_1$. (c, d) Plots of magnetization as a function of $J_2/J_1$ at different fixed magnetic fields $H=1.5$ and $H=2.5$. The horizontal dashed line indicates the classical phase transition.
• Figure 3: Low-field magnetization curve at $J_2/J_1=\frac{1}{8}$ obtained via VMC calculations performed on the $18\times18$ triangular lattice with PBC. The plateau at $m=0$ is due to the finite-size gap of the $Q=1$ monopole excitation. A clear first order transition from the monopole to the Y phase is observed, and the latter continuously evolves into the UUD.
• Figure S1: The four three-sublattice states investigated. Note that the umbrella (U) state is non-coplanar compared to Y, V and UUD state.
• Figure S2: The four four-sublattice states investigated.