Abstract
We study the nonequilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder. For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density and residual energy for a slow linear quench. We provide a general expression for the scaling of generated during a slow power-law dynamics, characterized by a rate and exponent , from a gapped phase to an anisotropic quantum critical point in dimensions, for which the energy gap for momentum components and for the rest components with : . These general expressions reproduce both the corresponding results for the Kitaev model as a special case for and and the well-known scaling laws of and for isotropic critical points for . We also present an exact computation of all nonzero, independent, multispin correlation functions of the Kitaev model for such a quench and discuss their spatial dependence. For the disordered Kitaev model, where the disorder is introduced via random choice of the link variables in the model’s fermionic representation, we find that and for a slow linear quench ending in the gapless (gapped) phase. We provide a qualitative explanation of such scaling.
4 More- Received 9 September 2010
DOI:https://doi.org/10.1103/PhysRevB.82.174305
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