Topological Hubbard model and its high-temperature quantum Hall effect

Abstract

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.

11 pages, 5 figures

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• 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
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Nearly flat band with Chern number C=2 on the dice lattice
• The insulator/Chern-insulator transition in the Haldane model

Cited by in corpus (33)

• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Zoology of Fractional Chern Insulators
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
• Topological Hamiltonian as an Exact Tool for Topological Invariants
• Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Noncommutative geometry for three-dimensional topological insulators
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Two-component quantum Hall effects in topological flat bands
• DMRG study of strongly interacting ${\mathbb{Z}}_2$ flatbands: a toy model inspired by twisted bilayer graphene
• Interaction driven quantum phase transition in fractional quantum spin Hall effects
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Ferromagnetism and spin excitations in topological Hubbard models with a flatband
• Tunable Chern insulator with shaken optical lattices
• Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands
• Elementary formula for the Hall conductivity of interacting systems
• Flat-band ferromagnetism in a topological Hubbard model
• Tuning the topological insulator states of artificial graphene
• $Z_2$ fractionalized Chern/topological insulators in an exactly soluble correlated model
• Ferromagnetism and Antiferromagnetism of Correlated Topological Insulator with Flat Band
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Current enhancement through a time dependent constriction in fractional topological insulators
• Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid
• Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
• Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) $\pi$-flux Hubbard model on honeycomb lattice
• Invisible flat bands on a topological chiral edge