Topological Hubbard model and its high-temperature quantum Hall effect

TL;DR

This paper investigates a time-reversal symmetric Hubbard model on a planar lattice, revealing that strong interactions induce simultaneous ferromagnetic order and a quantized charge Hall effect at half filling, with potential high-temperature applications.

Contribution

It introduces a novel variant of the Hubbard model supporting a high-temperature, interaction-driven quantum Hall effect with spontaneous magnetic order.

Findings

At 1/2 filling, the ground state exhibits ferromagnetic order.

A quantized charge Hall effect emerges without external magnetic fields.

The effect persists at high temperatures with strong interactions.

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.