Critical properties of the Kitaev-Heisenberg model

TL;DR

This paper investigates the finite-temperature critical behavior of the Kitaev-Heisenberg model on a honeycomb lattice, revealing two phase transitions and an intermediate critical phase likely observed in iridate compounds.

Contribution

It provides the first detailed analysis of the finite-temperature phase diagram of the Kitaev-Heisenberg model, identifying an intermediate critical phase with variable exponents.

Findings

Two phase transitions as temperature varies.

Existence of an intermediate critical Kosterlitz-Thouless phase.

Observation of the intermediate phase in real compounds Na$_2$IrO$_3$ and Li$_2$IrO$_3$.

Abstract

We study critical properties of the Kitaev-Heisenberg model on the honeycomb lattice at finite temperatures which might describe the physics of the quasi two-dimensional compounds, Na$_2$IrO$_3$ and Li$_2$IrO$_3$. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by order-by-disorder mechanism. Magnetically ordered state with the spontaneously broken $Z_6$ symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature ordered phase and the high-temperature disordered phase. The finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We argue that the intermediate phase has been actually observed above the low-temperature magnetically ordered phase in Na$_2$IrO$_3$, and likely in Li$_2$IrO$_3$.