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Fabien Trousselet(a), Peter Horsch(a), Andrzej M. Oles(a,b) and Giniyat Khaliullin(a)
(a) Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany (b) Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, PL-30059 Kraków, Poland We consider two formally related models of spins ½ on bidimensional lattices: the first is on the square lattice consisting of compass interactions - which select locally an easy-axis depending on the bond direction - coexisting with (nearest-neighbour) Heisenberg couplings, and the other being its counterpart on the honeycomb lattice, with compass couplings generalised to those of the Kitaev model. In the first case [1], we investigate to what extent the properties of the compass model - which, besides its motivations from orbital physics, can describe various candidate devices for quantum computing - are sensitive to perturbing interactions of Heisenberg type. We find that any finite Heisenberg amplitude removes the macroscopic degeneracy of ground states characteristic of the compass model, by selecting, among those, two particular states corresponding to an ordered phase with Z2 symmetry. We present the phase diagram of the model, with various ordered phases depending on the signs of couplings considered; in these phases, spin waves as found by exact diagonalisations for up to N=32 sites are well described by the linear spin-wave theory. Besides, for small Heisenberg couplings another type of excitations are observed in the low-energy spectrum of finite clusters: excitations, which are a property of the compass model and are grouped in dispersionless branches of states which could serve to define and manipulate qubits by acting on determined columns. We derive a size-dependent criterion on the relative coupling amplitudes, which is a necessary condition for the use of such a device for quantum computing. The related model on the honeycomb lattice, with Kitaev and Heisenberg interactions, has been previously studied as an effective model for some materials with large spin-orbit coupling and presenting a pseudospin liquid phase for small enough Heisenberg couplings and stripe-ordered phase if those are increased [2]. We analyse here the influence of non magnetic defects in such a system, with the motivation to know whether they favour one phase with respect to the other. The effect of a weak uniform magnetic field is also analysed, to determine the zero-temperature phase diagram under field and also as a tool to investigate the structure of ground states in presence of defects. [1] F. Trousselet, A.M. Oles, P. Horsch, EPL 91, 40005 (2010). [2] J. Chaloupka, G. Jackeli, G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010). |
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