Exactly solvable model of topological insulator realized on spin-$\tfrac{1}{2}$ lattice

Abstract

In this paper we propose an exactly solvable model of a topological insulator defined on a spin-$\tfrac{1}{2}$ square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin-$\tfrac{1}{2}$ Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model’s ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem’s spectrum from band to flat-band states.