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1. Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid

   https://doi.org/doi.org/10.1103/PhysRevX.11.011034  

   Wen-Han Kao, Johannes Knolle ( February 2021 , PRX action)

   null (Ed.)

   The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H3LiIr2O6 has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H3LiIr2O6. 

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2. Topological and magnetic phase transitions in the bilayer Kitaev-Ising model

   https://doi.org/10.1103/PhysRevB.109.024439  

   Vijayvargia, Aayush ; Seifert, Urban F. ; Erten, Onur ( January 2024 , Physical Review B)

   We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite signs of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped Z2 spin-liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120∘ compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along the z axis or lying in the xy plane. In both cases, our analysis reveals the formation of one-dimensional Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids. 

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3. Anderson–Kitaev spin liquid

   https://doi.org/10.1038/s41535-020-00285-3  

   Yamada, Masahiko G. ( November 2020 , npj Quantum Materials)

   The bond-disordered Kitaev model attracts much attention due to the experimental relevance inα-RuCl₃andA₃LiIr₂O₆(A= H, D, Ag, etc.). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions. The quantization of the thermal Hall conductivityκ^xy/Tdisappears by a quantum Hall transition induced by a small disorder, andκ^xy/Tshows a rapid crossover into a state with a negligible Hall current. We call this immobile liquid state Anderson–Kitaev spin liquid (AKSL). Especially, the critical disorder strengthδJ_c1~ 0.05 in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids.

    

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4. Vison crystals, chiral, and crystalline phases in the Yao-Lee model

   https://doi.org/10.1103/PhysRevB.108.224427  

   Akram, Muhammad ; Nica, Emilian Marius ; Lu, Yuan-Ming ; Erten, Onur ( December 2023 , Physical Review B)

   We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground-state phase diagram that consists of a variety of vison crystals with periodic arrangements of background Z2 flux (i.e., visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number ν and an associated chiral central charge c=ν/2 of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. For the bilayer systems, we find that interlayer coupling can also stabilize new topological phases. Our results spotlight the tunability and the accompanying rich physics in exactly solvable spin-orbital generalizations of the Kitaev model. 

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5. Sleuthing out exotic quantum spin liquidity in the pyrochlore magnet Ce2Zr2O7

   https://doi.org/10.1038/s41535-022-00458-2  

   Bhardwaj, Anish ; Zhang, Shu ; Yan, Han ; Moessner, Roderich ; Nevidomskyy, Andriy H. ; Changlani, Hitesh J. ( May 2022 , npj Quantum Materials)

   The search for quantum spin liquids—topological magnets with fractionalized excitations—has been a central theme in condensed matter and materials physics. Despite numerous theoretical proposals, connecting experiment with detailed theory exhibiting a robust quantum spin liquid has remained a central challenge. Here, focusing on the strongly spin-orbit coupled effectiveS = 1/2 pyrochlore magnet Ce₂Zr₂O₇, we analyze recent thermodynamic and neutron-scattering experiments, to identify a microscopic effective Hamiltonian through a combination of finite temperature Lanczos, Monte Carlo, and analytical spin dynamics calculations. Its parameter values suggest the existence of an exotic phase, aπ-flux U(1) quantum spin liquid. Intriguingly, the octupolar nature of the moments makes them less prone to be affected by magnetic disorder, while also hiding some otherwise characteristic signatures from neutrons, making this spin liquid arguably more stable than its more conventional counterparts.

    

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