Electrical Transport in the Hatsugai-Kohmoto Model

TL;DR

This paper investigates the electrical transport properties of the Hatsugai-Kohmoto model, revealing that traditional Kubo formulas fail to accurately describe susceptibilities and transport, while flux threading uncovers size-dependent currents that can be diamagnetic or paramagnetic.

Contribution

It demonstrates that in the Hatsugai-Kohmoto model, flux threading reveals size-dependent currents, challenging conventional transport calculations.

Findings

Kubo formulas do not reproduce correct susceptibilities.

Flux threading reveals size-dependent currents in the model.

Currents can be diamagnetic or paramagnetic.

Abstract

We show that in models with the Hatsugai-Kohmoto type of interaction that is local in momentum space thus infinite-range in real space, Kubo formulas neither reproduce the correct thermodynamic susceptibilities, nor yield sensible transport coefficients. Using Kohn's trick to differentiate between metals and insulators by threading a flux in a torus geometry, we uncover the striking property that Hatsugai-Kohmoto models with an interaction-induced gap in the spectrum sustain a current that grows as the linear size at any non-zero flux and which can be either diamagnetic or paramagnetic.