Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model

Abstract

The notion of a dynamical quantum phase transition (DQPT) was recently introduced in [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the non-analytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model are studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS-type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the non-degenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.

References in corpus (7)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Topological classification of dynamical phase transitions
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• First order dynamical phase transitions
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Quench dynamics and defect production in the Kitaev and extended Kitaev models

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