$Z_{2}$ fractionalized Chern/topological insulators in an exactly soluble correlated model

TL;DR

This paper introduces an exactly solvable 2D honeycomb lattice model revealing a novel $Z_2$ fractionalized Chern insulator phase with distinct edge state signatures, phase transition characteristics, and potential extensions.

Contribution

It presents the first exactly solvable model demonstrating a $Z_2$ fractionalized Chern insulator, differentiating it from conventional fractional Chern insulators and exploring phase transition properties.

Findings

Identification of a $Z_2$ fractionalized phase with gapped edge states.

Phase transition falls into the 3D Ising universality class.

Edge states exhibit strong Luttinger liquid behavior near criticality.

Abstract

In this paper we propose an exactly soluble model in two-dimensional honeycomb lattice, from which two phases are found. One is the usual Chern/topological insulating state and the other is an interesting $Z_2$ fractionalized Chern/topological insulator. While their bulk properties are similar, the edge-states of physical electrons are quite different. The single electron excitation of the former shows a free particle-like behavior while the latter one is gapped, which provides a definite signature to identify the fractionalized states. The transition between these two phases is found to fall into the 3D Ising universal class. Significantly, near the quantum transition point the physical electron in the edge-states shows strong Luttinger liquid behavior. An extension to the interesting case of the square lattice is also made. In addition, we also discuss some relationship between our exactly soluble model and various Hubbard-like models existing in the literature. The essential difference between the proposed $Z_{2}$ fractionalized Chern insulator and the hotly pursued fractional Chern insulator is also pointed out. The present work may be helpful for further study on the fractionalized insulating phase and related novel correlated quantum phases.