Phase diagram of the Kitaev-Hubbard model: $\mathbb{Z}_2$ slave-spin and QMC approaches

TL;DR

This paper maps out the phase diagram of the Kitaev-Hubbard model, revealing a quantum spin liquid phase and multiple magnetic transitions using advanced theoretical and computational methods.

Contribution

It provides the first comprehensive phase diagram of the KHu model employing $ ext{Z}_2$ slave-spin mean-field theory and auxiliary field quantum Monte Carlo.

Findings

Identification of a quantum spin liquid phase for specific parameters.

Detection of multiple magnetic phase transitions within the Mott phase.

Demonstration of the Mott transition via quasiparticle weight vanishing.

Abstract

Recent experiments show that the ground state of some layered materials with localized moments is in close proximity to the Kitaev spin liquid, calling for a proper model to describe the measurements. The Kitaev-Hubbard (KHu) model is the minimal model that captures the essential ingredients of these systems; it yields the Kitaev-Heisenberg spin model at the strong coupling limit and contains the charge fluctuations present in these materials as well. Despite its relevance, the phase diagram of the KHu model has not been rigorously revealed yet. In this work, we study the full phase diagram of the KHu model using the $\mathbb{Z}_2$ slave-spin mean-field theory as well as the auxiliary field quantum Monte Carlo on rather large systems and at low temperatures. The Mott transition is signaled by a vanishing quasiparticle weight evaluated using the slave-spin construction. Moreover, we demonstrate that there are multiple magnetic phase transitions within the Mott phase including magnetically ordered phases and most notably a quantum spin liquid phase for $1.0 \lesssim t^{\prime}/t \lesssim 1.11 $ at $U/t=5$.