Emergence of quantum spin liquid and spin-flop phase in Kitaev antiferromagnets in a [111] magnetic field

TL;DR

This work addresses the unresolved quantum phase diagram of the antiferromagnetic Kitaev model in a $[111]$ magnetic field, including the impact of off-diagonal $\Gamma$ interactions. Using unbiased exact diagonalization on a $C_{6}$-symmetric 24-site honeycomb cluster, the authors map the Kitaev-$Γ$ phase diagram and employ the hexagonal plaquette flux density $\overline{W}_{p}$ and the Kitaev-Preskill topological entanglement entropy $\gamma_E$ as phase-sensitive diagnostics. They identify a scalar chiral phase and two vector chiral intermediate phases, whose presence and extent depend on $\Gamma$, as well as a proximate quantum spin liquid with high $\gamma_E$ and a three-peak specific heat, plus a field-induced spin-flop phase with double-peak specific heat and logarithmic scaling. These results shed light on the nature and detectability of intermediate phases in AFM Kitaev magnets and provide guidance for experiments on candidate materials and for future large-scale simulations. The findings also highlight the sensitivity of intermediate-phase structure to field orientation and $\Gamma$, underscoring the need for precise control in experiments and more extensive numerical studies.

Abstract

Kitaev magnets have emerged as pivotal systems for investigating frustrated magnetism, providing a unique platform to explore quantum phases governed by the interplay between bond-dependent anisotropy and external magnetic fields. However, the quantum phase diagrams, particularly near the dominant antiferromagnetic Kitaev regime, remain puzzling despite extensive studies. In this work, we perform unbiased exact diagonalization calculations of the Kitaev-$Γ$ model in a [111] magnetic field on a $C_{6}$-symmetric 24-site cluster. By calculating the $\mathbb{Z}_2$ flux density and the topological entanglement entropy, we reveal multiple phase transitions and identify signatures of both scalar and vector chiral orders in the intermediate-field regime between the Kitaev spin liquid and the polarized phase. As the negative $Γ$ interaction increases, we discover a proximate quantum spin liquid featured by a three-peak specific heat and a spin-flop phase at a moderate magnetic field. Our findings provide insight into the field-induced intermediate phases in the antiferromagnetic Kitaev model and pave the way for the hunt for emergent phases in real materials.

Figures (15)

• Figure 1: (a) Illustration of the hexagonal plaquette operator $\hat{W_{p}}$. The nearest-neighbor links are distinguished as X (red), Y (green), and Z (blue) bonds, respectively. (b) The three-region partition scheme employed in calculating topological entanglement entropy using the Kitaev-Preskill method, with the red, green, and blue representing regions $A$, $B$, and $C$, respectively. (c) and (d) present the quantum phase diagrams obtained from the flux density $\overline{W}_{p}$ and TEE $\gamma_E$, respectively. The open circles represent the transition points while the crosses denote a partition within the KQSL. The symbol $\mathbf{\kappa_{v}}$ denotes regions with large vector spin chirality. The orange and red arrows indicate the regions of the vector chiral phases with ground-state degeneracies of two and three, respectively. Two special cutting lines, $h = 5 \phi/\pi$ (in yellow) and $h = 0.5\sqrt{1 - \phi/\pi}$ (in purple), are plotted for later use.
• Figure 2: The energy-level splitting $\delta E_g$ (left axis, red circles) and the ground-state fidelity $\mathcal{F}(\phi, h)$ (right axis, blue squares) as a function of $\phi$ along the parameter path $h = 5\phi/\pi$. The inset magnifies $\delta E_g$ in the region where $0.01 \leq \phi/\pi \leq 0.03$.
• Figure 3: (a) and (b) show the specific heat $C_v$ and the thermal entropy $S$ at two characteristic parameter points, ($\phi / \pi = 0.01$, $h = 0.05$) and ($\phi / \pi = 0.03$, $h = 0.15$), along the path line $h =5 \phi/\pi$. The shaded regions mark the estimated errors in the low-temperature regime.
• Figure 4: (a) The flux density $\overline{W}_{p}$ as a function of $h$ along parameter lines $\phi/\pi = 0.00$ (red circles) and 0.01 (blue squares). The insets show a magnified view in the range of $0.5 \leq h \leq 0.7$. (b) The same as (a) but for the TEE $\gamma_E$.
• Figure 5: (a) The scalar chiral order parameter $\chi_s$ as a function of $h$ along parameter lines $\phi/\pi = 0.00$ (red circles) and 0.01 (blue squares). (b) The same as (a) but for the vector chiral order parameter $\mathbf{\kappa_v}$.