Exact analysis of the interplay of charge order and unconventional pairings in the 2D Hatsugai-Kohmoto model

TL;DR

This paper analyzes the 2D Hatsugai-Kohmoto model to understand how charge order and unconventional pairing phenomena emerge and interact under various physical conditions, using an exactly solvable approach.

Contribution

It provides the first exact analysis of competing charge and pairing orders in the 2D HK model, revealing how external factors influence their interplay.

Findings

Charge-density wave and pair-density wave orders are intertwined at strong couplings.

Magnetic fields promote charge order and secondary pair-density wave formation.

Strain favors unidirectional pair-density wave over stripe-like charge order.

Abstract

We provide here a study of some competing ordering tendencies exhibited by the exactly solvable 2D Hatsugai-Kohmoto (HK) model on a square lattice. To this end, we investigate the interplay between superconductivity, charge-density wave (CDW) and pair-density wave (PDW) orders as a function of interaction, doping parameter, magnetic field, and uniaxial strain. As a result, we confirm the intertwined nature of CDW and PDW fluctuating orders for intermediate-to-strong couplings. We also verify that, while an applied magnetic field favors the formation of a CDW and allows the subsequent emergence of a PDW as a secondary order, strain effects favor unidirectional PDW as a primary order over the subdominant appearance of a stripe-like CDW. These results underscore the value of the HK model as an interesting platform in order to investigate (via an exactly solvable framework) the emergence of charge order and unconventional superconductivity in fermionic systems with strong interactions. Finally, we briefly discuss an orbital generalization of the HK model, which has been recently argued to be relevant to describe the properties of realistic strongly correlated systems.