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arXiv:2004.09622 · Physical review. B./Physical review. B

Ground-state properties of the K−Γ model on a honeycomb lattice

Takuto Yamada, Takafumi J. Suzuki, Sei-ichiro Suga

Published Jul 13, 2020• 13 citations
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Abstract

We investigate the ground-state properties of the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model on a honeycomb lattice using series expansions and numerical exact diagonalizations, where the model includes Kitaev ($K$) and symmetric off-diagonal ($\mathrm{\ensuremath{\Gamma}}$) interactions. Starting from the weakly interacting dimers on the specific bond, we strengthen the interdimer interactions to the isotropically interacting system. We show that depending on $\mathrm{\ensuremath{\Gamma}}$ and $K$, the dimer state survives up to the isotropically interacting system, where the phase transition occurs or obeys a phase transition to a magnetically ordered state at an anisotropic interaction. The results are summarized in the phase diagram. We also show that the Kekul\'e dimerized state is unstable in the isotropic $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model.

DOI
10.1103/physrevb.102.024415

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We investigate the ground-state properties of the K\ensuremath−\ensuremathΓK\ensuremath{-}\mathrm{\ensuremath{\Gamma}}K\ensuremath−\ensuremathΓ model on a honeycomb lattice using series expansions and numerical exact diagonalizations, where the model includes Kitaev (KKK) and symmetric off-diagonal (\ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ) interactions. Starting from the weakly interacting dimers on the specific bond, we strengthen the interdimer interactions to the isotropically interacting system. We show that depending on \ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ and KKK, the dimer state survives up to the isotropically interacting system, where the phase transition occurs or obeys a phase transition to a magnetically ordered state at an anisotropic interaction. The results are summarized in the phase diagram. We also show that the Kekul'e dimerized state is unstable in the isotropic K\ensuremath−\ensuremathΓK\ensuremath{-}\mathrm{\ensuremath{\Gamma}}K\ensuremath−\ensuremathΓ model.
In this paper, we investigate the ground-state phase diagram of the S=1/2S=1/2S=1/2 Heisenberg-$\mathrm{\ensuremath{\Gamma}}$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: A Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range-ordered states by the infinitesimal interchain interaction except for the case where the Heisenberg interaction is much weaker than the off-diagonal symmetric $(\mathrm{\ensuremath{\Gamma}})$ interaction. Starting from the isolated dimer limit, a triplet dimer phase survives up to the isotropically interacting system in a large part of the phase diagram where the Heisenberg and $\mathrm{\ensuremath{\Gamma}}$ interactions are ferromagnetic and antiferromagnetic, respectively. Otherwise, a phase transition to a magnetically ordered phase occurs before the interaction becomes isotropic. This indicates that the quantum spin liquid proposed in the $\mathrm{\ensuremath{\Gamma}}$ model [A. Catuneanu et al., npj Quantum Mater. 3, 23 (2018)] is unstable against the anisotropy of the interactions.
The theoretical inception of the Kitaev honeycomb model has had defining influence on the experimental hunt for quantum spin liquids, bringing unprecedented focus onto the synthesis of materials with bond-directional interactions. Numerous Kitaev materials, which are believed to harbor ground states parametrically close to the Kitaev spin liquid, have been investigated since. Yet, in these materials the Kitaev interaction often comes hand in hand with off-diagonal $\mathrm{\ensuremath{\Gamma}}$ interactions---with the competition of the two potentially giving rise to a magnetically ordered ground state. In an attempt to aid future material investigations, we study the phase diagram of the spin-1/2 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice. Employing a pseudofermion functional renormalization group (pf-FRG) approach, which directly operates in the thermodynamic limit and captures the joint effect of thermal and quantum fluctuations, we unveil the existence of extended parameter regimes with emergent incommensurate magnetic correlations at finite temperature. We supplement our results with additional calculations on a finite cylinder geometry to investigate the impact of periodic boundary conditions on the incommensurate order, thereby providing a perspective on previous numerical studies on finite systems.
We consider an extension of the Kitaev honeycomb model based on arbitrary dimer coverings satisfying matching rules. We focus on three different dimer coverings having the smallest unit cells for which we calculate the ground-state phase diagram. We also study one- and two-vortex properties for these coverings in the Abelian phases and show that vortex–vortex interactions can be attractive or repulsive. These qualitative differences are confirmed analytically by high-order perturbative expansions around the isolated-dimer limit. Similarities and differences with the original Kitaev honeycomb model are discussed.
Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g., the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models---Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice---or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size periodic lattices.