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Optical lattice systems offer the possibility of creating and tuning Diracpoints which are present in the tight-binding lattice dispersions. For example,such a behavior can be achieved in the staggered flux lattice or honeycomb typeof lattices. Here we focus on the strongly correlated bosonic dynamics in thevicinity of Dirac points. In particular, we investigate bosonic Mott insulatorphase in which quasiparticle excitations have a simple particle-holeinterpretation. We show that linear response dynamics around Dirac points, canbe significantly engineered at least in two ways: by the type of externalperturbation or by changing the lattice properties. The key role is played bythe interband transitions. Moreover, we explain that the behavior of thesetransitions is directly connected to different energy scales of the effectivehopping amplitudes for particles and holes. Presented in this work theoreticalstudy about tunability of linear response dynamics near the Dirac points can bedirectly simulated in the optical lattice systems.

Tuning linear response dynamics near the Dirac points in the bosonic Mott insulator