Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties

TL;DR

This study investigates small clusters in the Kitaev-Heisenberg-$\Gamma$ system to understand how competing interactions influence static properties, revealing phenomena like correlation plateaus and non-monotonic behaviors relevant to experimental observations.

Contribution

It provides detailed analysis of static properties in small clusters of the Kitaev-Heisenberg-$\Gamma$ system, highlighting effects of interaction signs and magnitudes under magnetic fields for the first time.

Findings

Plateaus in correlation functions with AF Heisenberg interaction

Non-monotonic correlation behavior with FM Heisenberg interaction

Insights into low energy spectrum, flux, magnetization, susceptibility, and heat capacity

Abstract

Recently, the Kitaev-Heisenberg-$\Gamma$ system has been used to explore various aspects of Kitaev spin liquid physics. Here, we consider a few small clusters of up to twelve sites and study them in detail to unravel many interesting findings due to the competition between all possible signs and various magnitudes of these interactions under the influence of an external magnetic field. When Heisenberg interaction is taken anti-ferromagnetic, one obtains plateaus in correlation functions where, surprisingly, the exact groundstate reduces to the eigenstate of Heisenberg interaction as well. On the other hand, for ferromagnetic Heisenberg interaction, its competition with Kitaev interaction results in non-monotonicity in the correlation functions. We discuss, in detail, the competing effects on low energy spectrum, flux operator, magnetization, susceptibility, and specific heat. Finally, we discuss how our findings could be helpful to explain some of the recent experimental and theoretical findings in materials with Kitaev interactions.