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arXiv:1508.04598 · The European Physical Journal B

Dynamical merging of Dirac points in the periodically driven Kitaev honeycomb model

Utso Bhattacharya, Sayak Dasgupta, Amit Dutta

Published Oct 1, 2016• 9 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2016-70265-5

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The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.
We consider two-dimensional periodically driven systems of fermions with particle-hole symmetry. Such systems support non-trivial topological phases, including ones that cannot be realized in equilibrium. We show that a space-time defect in the driving Hamiltonian, dubbed a “time vortex,” can bind π Majorana modes. A time vortex is a point in space around which the phase lag of the Hamiltonian changes by a multiple of 2π. We demonstrate this behavior on a periodically driven version of Kitaev’s honeycomb spin model, where Z2{{\mathbb{Z}}}_{2}Z2​ fluxes and time vortices can realize any combination of 0 and π Majorana modes. We show that a time vortex can be created using Clifford gates, simplifying its realization in near-term quantum simulators.