Exchange-frustrated quadrupoles on the honeycomb lattice: Flavor-wave spectra, classical degeneracies and parton constructions

TL;DR

This paper investigates the frustrated quadrupolar Kitaev model on a honeycomb lattice, revealing classical degeneracies, effective low-energy theories, and potential quantum-disordered phases through various analytical and parton-based methods.

Contribution

It introduces a comprehensive analysis of the quadrupolar Kitaev model, uncovering classical degeneracies, gauge structures, and candidate quantum-disordered states, advancing understanding of frustrated $S=1$ systems.

Findings

Classical mean-field ground states are extensively degenerate.

Effective Hamiltonians depend on residual symmetries in anisotropic limits.

Majorana parton constructions suggest both gapped and gapless quantum-disordered phases.

Abstract

We study the quadrupolar Kitaev model, an $S=1$ honeycomb-lattice model with frustrated bond-dependent quadrupolar interactions. Using complementary methods and expanding around controlled limits, we uncover several intertwined structures. First, a semiclassical variational analysis based on $\mathrm{SU}(3)$ flavor theory reveals an extensively degenerate manifold of classical mean-field ground states, suggesting that quantum fluctuations may stabilize a quantum-disordered phase. Second, in the bond-anisotropic limit, perturbation theory is used to derive effective low-energy Hamiltonians, which crucially depend on the presence (or absence) of a residual symmetry $\mathcal{M}$ of combined lattice reflection and discrete spin rotation. A Majorana parton construction uncovers an exact $\mathbb Z_2$ gauge structure and motivates possible confined and deconfined phases driven by gauge-charge condensation, consistent with the effective theories obtained in anisotropic limit. Further, within the same parton formalism, different Majorana mean-field ans\"atze produce both gapless and gapped candidate quantum-disordered states, distinguished by linear versus projective implementations of $\mathcal M$. Our results highlight frustrated quadrupolar interactions as a route to quantum-disordered phases, relevant to $S \geq 1$ Kitaev materials and Rydberg-array quantum simulators.