Quantum and classical behavior of spin-
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 Kitaev models in the anisotropic limit

We investigate magnetic properties in the S = 1 Kitaev model in the anisotropic limit. Performing the fourth-order perturbation expansion with respect to the x-bonds, y-bonds, and magnetic field, we derive the effective Hamiltonian, where the low-energy physics should be described by the free spins with an effective magnetic field. Making use of the exact diagonalization method for small clusters, we discuss ground-state properties in the system complementary.

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“…First, we consider the S = 1 Kitaev model without the external magnetic field [8]. When |J x | |J y | and J z → ∞, h eff,x > 0 and h eff,y =0.…”

Section: Model and Resultsmentioning

confidence: 99%

Magnetic Properties of the S = 1 Kitaev Model with Anisotropic Interactions

Minakawa

Nasu

Koga

2020

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)

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“…As first proposed by Baskaran, Sen and Shankar [22] integer spin systems are unlikely to have Majorana fermions. The difference between integer and half integer spins is also highlighted in the work of Minakawa et al [25], who found that introducing large anisotropy between X, Y and Z bonds leads to a very different type of ground state in integer spin systems with no long-range entanglement as compared with halfinteger spin systems where similar anisotropy maps on to the well known Toric code model [2]. Numerical studies have found further evidence of a gap in the excitation spectra for integer spins and for field induced spin-liquid phases [23,24,[26][27][28][29][30][31][32][33][34][35] as well as of large nearly degenerate subspaces giving rise to entropy plateaus [23,24,36,37].…”

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confidence: 92%

Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies

Bradley,

Singh

2021

Preprint

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We study the spin-one Kitaev model on the honeycomb lattice in the presence of single-ion anisotropies. We consider two types of single ion anisotropies: A D111 anisotropy which preserves the symmetry between X, Y and Z bonds but violates flux conservation and a D100 anisotropy that breaks the symmetry between X, Y and Z bonds but preserves flux conservation. We use series expansion methods, degenerate perturbation theory, and exact diagonalization to study these systems. Large positive D111 anisotropy leads to a simple product ground state with conventional magnon-like excitations, while large negative D111 leads to a broken symmetry and degenerate ground states. For both signs there is a phase transition at a small |D111| ≈ 0.2 separating the more conventional phases from the Kitaev Spin Liquid phase. With large D100 anisotropy, the ground state is a simple product state, but the model lacks conventional dispersive excitations due to the large number of conservation laws. Large negative D100 leads to decoupled one-dimensional systems and many degenerate ground states. No evidence of a phase transition is seen in our numerical studies at any finite D100. Convergence of the series expansion extrapolations all the way to D100 = 0 suggests that the non-trivial Kitaev spin-liquid is a singular-limit of this type of single-ion anisotropy going to zero, which also restores symmetry between X, Y and Z bonds.

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“…While much interest has justifiably focused on spin-1/2 Kitaev materials, it has been shown that Kitaev models with arbitrary spin retain many interesting properties [20][21][22][23][24][25][26][27][28][29][30]. For arbitrary spin, the system is a classical spin-liquid at intermediate temperatures, with only very short-range spin correlations and an extensive classical degeneracy.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice

et al. 2021

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We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S = 1 and S = 2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T → 0, become critical as T → 0, or diverge exponentially as T → 0. The Z 2 flux variable associated with each hexagonal plaquette saturates at the value +1 as T → 0 in all models except the S = 1 antiferromagnet where the mean flux remains zero as T → 0. We provide qualitative explanations for these results.

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Quantum and classical behavior of spin- S Kitaev models in the anisotropic limit

Cited by 29 publications

References 84 publications

Magnetic Properties of the S = 1 Kitaev Model with Anisotropic Interactions

Magnetic Properties of the S = 1 Kitaev Model with Anisotropic Interactions

Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies

Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice

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