Perturbed vortex lattices and the stability of nucleated topological phases

Abstract

We study the stability of nucleated topological phases that can emerge when interacting non-Abelian anyons form a regular array. The studies are carried out in the context of Kitaev's honeycomb model, where we consider three distinct types of perturbations in the presence of a lattice of Majorana mode binding vortices -spatial anisotropy of the vortices, dimerization of the vortex lattice and local random disorder. While all the nucleated phases are stable with respect to weak perturbations of each kind, strong perturbations are found to result in very different behavior. Anisotropy of the vortices stabilizes the strong-pairing like phases, while dimerization can recover the underlying non-Abelian phase. Local random disorder, on the other hand, can drive all the nucleated phases into a gapless thermal metal state. We show that all these distinct behavior can be captured by an effective staggered tight-binding model for the Majorana modes. By studying the pairwise interactions between the vortices, i.e. the amplitudes for the Majorana modes to tunnel between vortex cores, the locations of phase transitions and the nature of the resulting states can be predicted. We also find that due to oscillations in the Majorana tunneling amplitude, lattices of Majorana modes may exhibit a Peierls-like instability, where a dimerized configuration is favored over a uniform lattice. As the nature of the nucleated phases depends only on the Majorana tunneling, our results are expected to apply also to other system supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave superconductors, Wigner crystals in Moore-Read fractional quantum Hall states or arrays of topological nanowires.

Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

“…Remarkably, (q * , r * ) becomes identical to (q c , r c ) (0.6813, 0.2679) at φ = 0, implying that the ground state is the critical LG state exhibiting macroscopic loops. Furthermore, its lowenergy physics is described by the Ising CFT [27] which is consistent with the expected one [20,[28][29][30]. Therefore, according to these circumstantial evidences, we may conclude that the LG ansatz at φ = 0 is the exact ground state.…”

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

“…This local gap is defined as in Eqs. (33) and (34), with the specific two-flux state obtained by flipping the (ij ) bond. We note that the selection rules for physical states continue to apply for the moderate disorder considered here.…”

“…(Brief discussions of disorder in the Kitaev model have been given in Refs. [7] and [34], and a Kitaev-style chiral spin-liquid model with random exchange was considered in Ref. [35].)…”

Kitaev spin models from topological nanowire networks

“…[39], where sufficient randomness of the signs is predicted to drive the system into a gapless thermal metal state. This mechanism has been shown to hold in the context of the honeycomb model [36] and thus it is expected to apply also in the variants of Kitaev spin models. Thus we predict that when L/ l π 2 /4 and ξ/ l 2, i.e., roughly when…”