$Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model

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.

13pages,no figures, some physics clarified and acknowledgement updated

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• Soluble limit and criticality of fermions in Z2 gauge theories
• Exactly Solvable Kondo Lattice Model in Anisotropic Limit
• Tuning the topological insulator states of artificial graphene
• Topological Green's function zeros in an exactly solved model and beyond
• Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Topological quantum phase transition in Kane-Mele-Kondo lattice model
• Notes on Quantum oscillation for Hatsugai-Kohmoto model
• Absence of coherent peaks in a $Z_2$ fractionalized BCS superconducting state