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Moving, merging and annihilating Dirac points are studied theoretically inthe tight-binding model on honeycomb lattice with up-to third-nearest-neighborhoppings. We obtain a rich phase diagram of the topological phase transitionsin the parameter space of direction-dependent hoppings. We obtain theconditions for the three Dirac points to merge and for the tricritical points.We find that only very small third-nearest-neighbor hoppings are enough for theexistence of the merging of three-Dirac-points and the tricritical points, ifthe system is sufficiently anisotropic. The density of states is obtained to be$D(\epsilon) \propto |\epsilon|^{1/3}$ when three Dirac points merge, and$D(\epsilon) \propto |\epsilon|^{1/4}$ at the tricritical points. It ispossible to realize these topological phase transitions in the ultracold atomson the optical lattice, strained monolayer graphene or strained bilayergraphene.

Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice