Quantum phase transition in Heisenberg-Kitaev model

Abstract

We explore the nature of the quantum phase transition between a magnetically ordered state with collinear spin pattern and a gapless Z 2 spin liquid in the Heisenberg-Kitaev model. We construct a slave particle mean-field theory for the Heisenberg-Kitaev model in terms of complex fermionic spinons. It is shown that this theory, formulated in the appropriate basis, is capable of describing the Kitaev spin liquid as well as the transition between the gapless Z 2 spin liquid and the so-called stripy antiferromagnet. Within our mean-field theory, we find a discontinuous transition from the Z 2 spin liquid to the stripy antiferromagnet. We argue that subtle spinon confinement effects, associated with the instability of gapped U (1) spin liquid in two spatial dimensions, play an important role at this transition. The possibility of an exotic continuous transition is briefly addressed.

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

“…After a preliminary set of runs, we find three different phases in this quadrant: FSL, stripy, and Néel as one moves from ϕ = −90 • to 0. Noting that this matches the results from previous studies [11,12,[30][31][32], it remains to verify how our results agree with the transition points found previously. Having obtained tensors representing the phases at the two extremes of the angle window shown in Fig.…”

“…This value is also reported in the extended formulation on a 24-site system [12]. The restricted formulation was also studied from a slave-particle mean field approach [30] where the behavior of the order parameter itself showed a discontinuity, yet it was suggested that the transition could indeed be of either second-or weak first-order type at a value of ϕ ≈ −72 • (α ≈ 0.76), owing to the lack of quantum fluctuations beyond the mean field level in their approach. Finally, a so-called mixed PEPS approach found a phase transition at ϕ ≈ −89 • (α ≈ 0.99) [32].…”

“…This model has been tackled in the past using a variety of approaches in different regions of its full parameter regime [11,12,[30][31][32]. In its original formulation [11] (covering only the region ϕ ∈ [−π/2,0]), small system studies [11,31] found either a second-or weak first-order phase transition joining a spin liquid phase to a so-called stripy phase at roughly ϕ ≈ −76 • (or α ≈ 0.8 in the original formulation) (see Fig.…”

Finite-temperature phase diagram of the classical Kitaev-Heisenberg model

“…This is because the Kitaev spin liquid is rather stable with respect to the Heisenberg interaction 2,12,14,18 ; it remains the ground state of the KH model for a wide range of strengths of the Heisenberg interaction. Exact diagonalization studies 2,12,14 suggest a stability of the spin liquid phase for the model parameter α in the range (0.8, 1), where α is determined such that J K = 2α and J H = 1−α.…”

“…Recently, Jackeli and Khaliullin 1 suggested that the Kitaev model could actually be realized within the honeycomb iridates with general formula A 2 IrO 3 , since the anisotropic part of the interactions among Ir-ions has the same form as the Kitaev coupling. This suggestion has triggered a lot of experimental [7][8][9][10][11] and theoretical [12][13][14][15][16][17][18] activity in the study of Na 2 IrO 3 and Li 2 IrO 3 compounds.…”