$Z_2$ 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.

arXiv comment13pages,no figures, some physics clarified and acknowledgement updated

References in corpus (47)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Symmetry protected topological orders and the group cohomology of their symmetry group
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Fractional Chern Insulator
• Braiding statistics approach to symmetry-protected topological phases
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Fractional topological insulators
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Boson topological insulators: A window into highly entangled quantum phases
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Integer quantum Hall effect for bosons: A physical realization
• Critical fermi surfaces and non-fermi liquid metals
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Zoology of Fractional Chern Insulators
• Fractionalization, topological order, and cuprate superconductivity
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Symmetry protected topological phases in non-interacting fermion systems
• Spin-charge Separated Solitons in a Topological Band Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator
• Orthogonal Metals: The simplest non-Fermi liquids
• Mutual Chern-Simons theory for Z_2 topological order
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Z_2-slave-spin theory for strongly correlated fermions
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Symmetry protected fractional Chern insulators and fractional topological insulators
• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
• Chiral Spin Liquid in Correlated Topological Insulator
• Fractional Chern Insulators from the nth Root of Bandstructure
• Topological Hubbard model and its high-temperature quantum Hall effect
• Alternative Kondo breakdown mechanism: Orbital-selective orthogonal metal transition
• Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal
• Topological antiferromagnetic spin-density-wave phase in an extended Kondo lattice model

Cited by in corpus (13)

• Interacting topological insulators: a review
• Orbitally induced hierarchy of exchange interactions in zigzag antiferromagnetic state of honeycomb silver delafossite Ag3Co2SbO6
• Topological order in a correlated Chern insulator
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• 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