Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice

Abstract

We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_2$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.

arXiv comment14 pages, 12 figures; title changed, only minor modifications in the text

References in corpus (46)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Experimental realization of a topological crystalline insulator in SnTe
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• The space group classification of topological band insulators
• Continuous Time Quantum Monte Carlo method for fermions
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Synthetic gauge fields in synthetic dimensions
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Bosonization for Beginners --- Refermionization for Experts
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
• Optical Flux Lattices for Ultracold Atomic Gases
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Interaction driven instabilities of a Dirac semi-metal
• Spin-charge Separated Solitons in a Topological Band Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• A study on correlation effects in two dimensional topological insulators
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Dynamic Optical Superlattices with Topological Bands
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Interacting two helical edge modes in quantum spin Hall systems
• Interaction effect in two-dimensional Dirac fermions
• Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges
• Manifestly gauge independent formulations of the Z2 invariants
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Realising Haldane's vision for a Chern insulator in buckled lattices
• Transport discovery of emerging robust helical surface states in $Z_2=0$ systems
• Competition of superfluidity and density waves in one-dimensional Bose-Fermi mixtures
• Spectral functions of two-band spinless fermion and single-band spin-1/2 fermion models
• Topological Mid-gap States of Topological Insulators with Flux-Superlattice

Cited by in corpus (13)

• Quantum Critical Points and the Sign Problem
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• First order topological phase transition of the Haldane--Hubbard model
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
• Phase transitions in the Haldane-Hubbard model
• Interacting weak topological insulators and their transition to Dirac semimetal phases
• The competition between the intrinsic and Rashba spin-orbit coupling and effects of correlations on Rashba SOC-driven transitions in the Kane-Mele model
• Entanglement studies of interacting fermionic models
• Phase transitions of the Kane-Mele-Hubbard model with a long-range hopping
• Multitude of phases in correlated lattice fermion systems with spin-dependent disorder
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Zeeman field induced corner states in the Kane-Mele-Hubbard model