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

TL;DR

This work addresses the field response of the spin-1/2 $J_1-J_2$ triangular-lattice Heisenberg antiferromagnet and the proximity to a zero-field quantum spin-liquid (QSL) phase. The authors combine large-scale density-matrix renormalization group (DMRG) simulations with self-consistent one-loop spin-wave theory to map the $J_2/J_1$--$B$ phase diagram and the stability of magnetization plateaux. They find that quantum fluctuations stabilize coplanar order across the phase diagram, producing a sequence of magnetization plateaux, and that near the QSL window ($0.06 \lesssim J_2/J_1 \lesssim 0.14$) the $m=1/3$ and $m=1/2$ plateaux overlap; SCOL reproduces DMRG results with quantitative accuracy. The results validate semiclassical parameterization of plateau phases and offer a practical framework to extract microscopic parameters from neutron scattering and to diagnose proximity to a QSL in triangular antiferromagnets.

Abstract

We investigate the spin-1/2 $J_1-J_2$ triangular-lattice Heisenberg antiferromagnet in a magnetic field by combining large-scale density matrix renormalization group (DMRG) simulations with self-consistent spin-wave theory. The resulting field-coupling phase diagram reveals that quantum fluctuations stabilize coplanar order across the entire parameter range, giving rise to a characteristic sequence of magnetization plateaux. Near the quantum-spin-liquid window $0.06 \lesssim J_2/J_1 \lesssim 0.14$, which extends to magnetic field $B \sim J_1$, we identify overlapping $m = 1/3$ and $m = 1/2$ plateaux - a distinctive hallmark of the system's proximity to the low-field spin-liquid regime. The excellent quantitative agreement between DMRG and self-consistent one-loop spin-wave calculations demonstrates that semiclassical approaches can reliably capture and parameterize the plateau phases of triangular quantum antiferromagnets.

Figures (8)

• Figure 1: Phase diagram of the model obtained using iDMRG on cylinders. See text for a detailed discussion of the phases.
• Figure 2: Structure factor $S({\bf q})-(S^z_{\rm tot})^2/N$ calculated on XC-8 cylinders in the representative (a) three sub-lattice Y phase, (b) two sub-lattice canted-stripes (CS) phase (c) four sub-lattice $\bar{\rm V}$ phase (d) QSL regime. Insets show scaling of the structure factor with number of sites, $N$, at the high symmetry points.
• Figure 3: (a) Magnetization as function of magnetic field for different ratios of $J_2/J_1$ featuring the 1/3 and 1/2 plateaux. (b) Phase boundaries of the magnetization plateaux as obtained using DMRG (solid line) and spin waves (SW) one-loop (OL) and self-consistend one-loop (SCOL) analysis (dotted and dashed line respectively). (c) Local magnetic moment in the 1/3 and (d) 1/2 magnetization plateaus.
• Figure 4: (a) An estimate for the local ordered moment $m_{\bf Q}$ obtained using DMRG (see text for details) as function of $J_2/J_1$ for different magnetic fields. Values obtained for ${\bf Q}={\bf K}$ (${\bf Q}={\bf M}$) are plotted as circles (squares). Error bars correspond to errors in extrapolation with $1/N_y$. The threshold value $m_{\rm th}=0.06$ used as an indicator of the quantum disordered regime is plotted as a red horizontal line. (b) QSL region obtained using DMRG (orange filled area) and spin-waves (red filled area). The area bounded by the red dashed curves with up (down) triangle markers corresponds to the region in which the local ordered moment on the 'tilted' (down) sublattice in the Y phase vanishes within linear spin-wave analysis. Similarly, the area bounded by the red dashed curve with square markers corresponds to the region in which the local ordered moment vanishes in the stripe phase. Inset shows the zero-field susceptibility of the Y and stripe states (solid line) as well as the cone state (dashed line) as function of $J_2$ obtained within the spin-wave analysis. Here $\chi_0=1/9$ is the classical value for the susceptibility in the Y phase.
• Figure 5: Transverse and longitudinal components of the structure factor in the (a) ${\bar{\rm Y}}$ and (b) ${\bar{\rm Y}}'$ states observed in the 4sl-Y region of the phase diagram in Fig. \ref{['fig:PhaseDiagram']}.