Critical Properties of the Kitaev-Heisenberg Model

Itamar Kimchi, Yi‐Zhuang You, Ashvin Vishwanath

Si-Qi Hou, Wei Wang, Shun-Li Yu +1 more

Craig Price, Natalia Borisovna Perkins

We study the critical properties of the Kitaev-Heisenberg model on the honeycomb lattice at finite temperatures that 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 the order-by-disorder mechanism. This magnetically ordered state with a 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. 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 observed above the low-temperature, magnetically ordered phase in Na(2)IrO(3), and also, likely exists in Li(2)IrO(3).

Francisco M. O. Brito, Aires Ferreira

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a Chebyshev iterative method that gives access to the thermodynamic properties and critical behavior of frustrated quantum spin models with good accuracy. The computational complexity scales linearly with the Hilbert space dimension and the number of Chebyshev iterations used to approximate the eigenstates. Using this approach, we calculate the spin correlations of the Kitaev-Heisenberg model, a paradigmatic model of honeycomb iridates that exhibits a rich phase diagram including a quantum spin liquid phase. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum (TPQ) states. All methods accurately predict a transition to a stripy (spin-liquid) phase for the critical value of the Kitaev coupling $ J_K \approx -1.3 J_H $ ($J_K \approx -8.0 J_H$) for honeycomb layers with ferromagnetic Heisenberg interactions ($J_{H}>0$). Our findings suggest that a hybrid Chebyshev-TPQ approach could open the door to previously unattainable studies of quantum spin models in two dimensions.

Johannes Reuther, Ronny Thomale, Simon Trebst

Katsuhiro Morita, Takami Tohyama

The authors investigate the finite-temper properties of the S=1/2 Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods. In both lattice models, the specific heat exhibits multiple-peak structures.