Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model

Abstract

Motivated by the largely unexplored domain of multi-polar ordered spin states in the Kitaev-Heisenberg (KH) systems we investigate the ground state dynamics of the spin-$\frac{1}{2}$ KH model, focusing on quadrupolar (QP) order in 2-leg ladder and two-dimensional honeycomb lattice geometries. Employing exact diagonalization and density-matrix renormalization group methods, we analyze the QP order parameter and correlation functions. Our findings reveal a robust QP order across a wide range of the phase diagram, influenced by the interplay between Heisenberg and Kitaev interactions. Notably, we observe an enhancement of QP order near Kitaev quantum spin liquid (QSL) phases, despite the absence of long-range spin-spin correlations. This highlights a complex relationship between QP order and QSLs, offering new insights into quantum magnetism in low-dimensional systems. Our findings provide a rational explanation for the observed nonlinear magnetic susceptibility in $\alpha$-RuCl${}_3$.

References in corpus (14)

• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Weyl spin liquids
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Kitaev magnetism through the prism of lithium iridate
• Multipolar phase in frustrated spin-1/2 and 1 chains
• Majorana correlations in the Kitaev model with ordered-flux structures