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1. Further insights into the thermodynamics of the Kitaev honeycomb model

   https://doi.org/doi.org/10.1103/PhysRevB.102.224402  

   Kexin Feng, Natalia B. (December 2020, PRB)

   null (Ed.)

   Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes. Using large-scale Monte Carlo simulations, we verify that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat. 

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2. Magnetic field effects on the quantum spin liquid behaviors of NaYbS2

   https://doi.org/10.1007/s44214-022-00011-z  

   Wu, Jiangtao; Li, Jianshu; Zhang, Zheng; Liu, Changle; Gao, Yong Hao; Feng, Erxi; Deng, Guochu; Ren, Qingyong; Wang, Zhe; Chen, Rui; et al (December 2022, Quantum Frontiers)

   Abstract Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides Equation missing<#comment/>(Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Equation missing<#comment/>and Equation missing<#comment/>ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Equation missing<#comment/>ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions. 

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3. Electronic structure of Co $3d$ states in the Kitaev material candidate honeycomb cobaltate ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ probed with x-ray dichroism

   https://doi.org/10.1103/PhysRevB.107.214443  

   van Veenendaal, M.; Poldi, E. H.; Veiga, L. S.; Bencok, P.; Fabbris, G.; Tartaglia, R.; McChesney, J. L.; Freeland, J. W.; Hemley, R. J.; Zheng, H.; et al (June 2023, Physical Review B)

   none (Ed.)

   The recent prediction that honeycomb lattices of Co2+ (3d7) ions could host dominant Kitaev interactions provides an exciting direction for exploration of new routes to stabilizing Kitaev’s quantum spin liquid in real materials. Na3Co2SbO6 has been singled out as a potential material candidate provided that spin and orbital moments couple into a Jeff = 1/2 ground state, and that the relative strength of trigonal crystal field and spin-orbit coupling acting on Co ions can be tailored. Using x-ray linear dichroism (XLD) and x-ray magnetic circular dichroism (XMCD) experiments, alongside configuration interaction calculations, we confirm the counterintuitive positive sign of the trigonal crystal field acting on Co2+ ions and test the validity of the Jeff = 1/2 description of the electronic ground state. The results lend experimental support to recent theoretical predictions that a compression (elongation) of CoO6 octahedra along (perpendicular to) the trigonal axis would drive this cobaltate toward the Kitaev limit, assuming the Jeff = 1/2 character of the electronic ground state is preserved. 

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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. Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

   https://doi.org/10.1038/s41467-023-40769-x  

   de la Torre, A.; Zager, B.; Bahrami, F.; Upton, M. H.; Kim, J.; Fabbris, G.; Lee, G. -H.; Yang, W.; Haskel, D.; Tafti, F.; et al (August 2023, Nature Communications)

   Abstract Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H₃LiIr₂O₆is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H₃LiIr₂O₆and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H₃LiIr₂O₆as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid. 

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