Exactly solvable model of topological insulator realized on spin-1/2 lattice

TL;DR

This paper introduces an exactly solvable model of a topological insulator on a spin-1/2 lattice, revealing novel quantum phase transitions without gap closing and detailed topological phase diagram analysis.

Contribution

It presents a new exactly solvable model combining fermions and spins, showing topological phases and phase transitions without gap closing, expanding understanding of topological insulators.

Findings

Topological phase transitions occur without gap closing.

The model's ground state exhibits a non-trivial topological phase.

Quantum phase transitions involve a spectrum rearrangement from band to flat-band states.

Abstract

In this paper we propose an exactly solvable model of a topological insulator defined on a spin-1/2 square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin-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.