Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods

TL;DR

This study explores the finite-temperature behavior of Kitaev-Heisenberg models on kagome and triangular lattices using advanced Lanczos methods, revealing multiple specific heat peaks and their origins related to magnetic correlations and quantum effects.

Contribution

The paper introduces improved finite-temperature Lanczos methods to analyze Kitaev-Heisenberg models, uncovering detailed thermal properties and differences in quantum fluctuation effects on different lattices.

Findings

Multiple peaks in specific heat indicate complex thermal behavior.

High-temperature peaks linked to crossover from paramagnetic to short-range order.

Order by disorder occurs in triangular but not kagome Kitaev models.

Abstract

Frustrated quantum spin systems such as the Heisenberg and Kitaev models on various lattices, have been known to exhibit various exotic properties not only at zero temperature but also for finite temperatures. Inspired by the remarkable development of the quantum frustrated spin systems in recent years, we investigate the finite-temperature properties of the $S=1/2$ Kitaev-Heisenberg models on kagome and triangular lattices by means of finite-temperature Lanczos methods with improved accuracy. In both lattices, multiple peaks are confirmed in the specific heat. To find the origin of the multiple peaks, we calculate the static spin structure factor. The origin of the high-temperature peak of the specific heat is attributed to a crossover from the paramagnetic state to a short-range ordered state whose static spin structure factor has zigzag or linear intensity distributions in momentum space. In the triangular Kitaev model, the "order by disorder" due to quantum fluctuation occurs. On the other hand, in the kagome Kitaev model it does not occur even with both quantum and thermal fluctuations.